What is the correct understanding of nitya-siddha (eternally liberated) and nitya-baddha (eternally conditioned)?

There is only one classification of jiva-souls (marginal living entities) who can choose remain "liberated" in the spiritual world (their natural infinite position).

Or become "conditioned" in the material world within the repeated cycle of birth and death, then, due to being frustrated with material existence, attempting to extinguish one's existence by entering the impersonal brahmajyoti, NOT two as some believe. 

This means each individual jiva-soul ALWAYS has "two-sides" to their unique character and personality.

1 - They nitya-baddha" (eternally conditioned [fallen] in the material world or the impersonal brahmajyoti).

2 - They can be "nitya-siddha" (eternally liberated in the Vaikuntha planets and Goloka-Vrindavana which are the jiva-soul's natural eternal original home)

The term "eternal" means ONLY while in that "liberated state" in the spiritual world, or while "conditioned" in the material world and impersonal brahmajyoti. 

This means the jiva-souls can choose for themselves to be with Krsna, or reject Krsna. 

Each jiva-soul, originally as part and parcel of the spiritual world, always have a choice of where they can live be it the spiritual world, the material world or try to extinguish their personality by entering the impersonal brahmajyoti. 

Srila Prabhupada - "So, unless there is a possibility of misusing our free will, there is no question of freedom." (Dialectical Spiritualism, Critique of Descartes)

Srila Prabhupada – "So everyone can know that independence means one can use it properly, or one can misuse it. That is independence. If you make it one way only, that is not independence; that is force." (Los Angeles, June 23, 1975)

Some wrongly claim there are "two types of jiva-souls," one only existing in the spiritual world, the other only existing in the material world which is nonsense-

1 - One who stays in the Vaikuṇṭha and Goloka Vṛndāvana and never fall down (by choice) to go to the decaying material creation (nitya-siddha)

2 - On who is in the material creation (nitya-baddha) eternally or can be dormant (inactive) in the impersonal Brahmajyoti. 

The nitya-baddhas can also enter the spiritual worlds too and become nitya-siddha, but once there can never fall down and be nitya-baddha again.

Therefore there is only one category of jiva-souls who have "two-sides" to their individual personality - 

1 - Nitya-siddha (eternally liberated).

2 - Nitya-baddha (eternally conditioned).

The jiva-souls can be either nitya-siddha (eternally liberated) or nitya-baddha (eternally conditioned), however, the jiva-soul's original position is nitya-siddha (eternally liberated), and the fallen condition of the jiva-soul is nitya-baddha (eternally conditioned). 

This means the jiva-soul's original home is Vaikuntha and Goloka-Vrindavana.

Srila Prabhupada - "In the broader sense everyone comes from Krsnaloka (Goloka-Vrindavana). When one forgets Krsna he is conditioned (nitya-baddha), when one remembers Krsna he is liberated (nitya-siddha)." (Letter to Mukunda, June 10, 1969)

As said above, there is only one category of the jiva-soul who can be either nitya-baddha (eternally conditioned) or nitya-siddha (eternally liberated). 

To make it clearer, there is only "one kind" of jiva-soul existing and they are ALL known as the "marginal living entities" in both the spiritual and material worlds. 

Srila Prabhupada - "The jiva-souls are always called marginal energy whether he is in the spiritual world or in the material world. There are instances where marginal energy jiva-souls have fallen from the spiritual world, just like Jaya and Vijaya. So the potency to fall under the influence of the lower energy is always there. And thus the individual jiva-soul is called as Krsna’s marginal energy." (Letter to Rayarama, Dec 2, 1968)

Srila Prabhupada - "The "immediate" expansions of the Lord are called svāṁśa or personal direct expansions (Visnu-tattva who are Krsna playing another role in His own pastimes) The "separated" expansions of the Lord are called vibhinnāṁśa (jiva-tattva or "independent" jiva-souls (marginal living entities) like us." (BG, Ch 10 Text 37, Purport)

Each individual jiva-soul (marginal living entity) in the spiritual world can "choose" to "voluntarily" serve Krsna in an unlimited variety of ways as an unlimited varieties of bodily forms, or can even reject Krsna if they choose to do so, and enter or return to the impermanent decaying  material world.

Srila Prabhupada – "The jiva-souls are Krsna’s marginal energy. Marginal energy means the jiva-souls (marginal living entities) may be under the control of the spiritual energy, or they may be under the control of material energy. But when the jiva-souls are under the control of the material energy, that is their precarious condition, struggle for existence. And when they are under spiritual energy, that is their original position and life of freedom." (Los Angeles, Nov 23, 1968)

Being "marginal" means the jiva-souls can always choose to be under the influence of the spiritual energy or under the material energy or choose to be either nitya-siddha or nitya-baddha.

Srila Prabhupada - "There are two kinds of marginal living entities: nitya-siddha and nitya-baddha. The actual constitutional position of EVER marginal living entity is nitya-siddha." (CC lecture, July 13, 1976) 

Srila Prabhupada - "By following the rules and regulations and instructions of the spiritual master, he can become again nitya-siddha. So the Krsna consciousness movement is to make the nitya-baddhas AGAIN nitya-siddha." (New York Lecture CC, July 13, 1976)

Srila Prabhupada - "So the Krsna consciousness movement is to make the nitya-baddhas AGAIN nitya-siddha, to bring them to their original position. It is a difficult task." (London lecture BG, 13-14, July 14, 1973)

Srila Prabhupada - "Nitya-baddhas are within this material world. Beginning from Brahma down to a small ant, insignificant ant, they are all nitya-baddha. Anyone who enters the material world, they are nitya baddha." (Lecture BG, 13-14, July 14, 1973)

Srila Prabhupada – "Regarding your questions about how and from where did the conditioned souls fall, your first question if someone has a relationship with Lord Krsna on Krsnaloka (Goloka Vrindavana), does he ever fall down? The souls are endowed with minute independence as part of their nature and this minute independence may be utilized rightly or wrongly at anytime, so there is always a chance of falling down by misuse of one’s independence." (Letter to Jagadisa Dasa, 25th April 1970)

Srila Prabhupada – "These spirit souls and all spirit souls are coming from Vaikuntha, but in these material worlds they are taking various grades of bodies according to their material activities. There is no new souls. New and old are due to this material body, but the soul is never born and never dies, so if there is no birth how there can be new soul." (Letter to Jagadisa Dasa, 9th July 1970)

Srila Prabhupada - "Regarding your questions concerning the spirit souls falling into Maya’s influence, it is not that those who have developed a passive relationship with Krsna are more likely to fall into nescient activities, usually anyone who has developed his relationship with Krsna does not fall down in any circumstance, but because the independence is always there, the soul may fall down from any position or any relationship by misusing his independence." (Letter to Jagadisa Dasa, 27th Feb 1970)

Srila Prabhupada - "But his relationship with Krsna is never lost, simply forgotten by the influence of maya, it maybe regained or revived by the process of hearing the Holy Name of Krsna and then the devotee engages himself in the service of the Lord which is his original constitutional position (Nitya-siddha). The relationship of the living entity with Krsna is eternal as both Krsna and the living entity are eternal; the process is one of revival only, nothing new." (Letter to Jagadisa Dasa, 27th Feb 1970)

Genuine meaningful loving exchanges are voluntary in a reciprocal "two-way" relationship, it is never a "one-way" forceful dictatorship where Krsna possess you and does all the thinking and actions for you, that is NOT surrender, it is impersonalism.

Surrender to Krsna's pure devotees does not mean you lose your free will, the independence of voluntary service, the ability to think for yourself, and unique individuality in the spiritual world, no, mindless bogus surrender is impersonalism!  

The jiva-souls (marginal living entities) are eternal PERSONS, as a spiritual bodily form like Krsnas Body, whose perpetual permanent natural home is the spiritual world.

All individual jīva-souls are ETERNAL persons therefore there are no new jiva-souls being created because they have ALWAYS existed meaning they are beginningless and endless.

God (Krsna) is not ONLY an all-pervading consciousness who is even in the atom, no, Krsna the Supreme Personality of Godhead and cause of all causes is also simultaneously an individual "PERSON" as an eternal spiritual bodily Form, who's Bodily rays ARE the Brahmajyoti.

Srila Prabhupada - "The spirit soul is NOT formless; it has got form, the spirit soul always has form and is expressed as hands, legs, heads, everything. But with our material eyes at the present, our gross eyes, we cannot see these facts; therefore we foolishly believe the jiva-souls have no form." (Lecture BG, Ch 2 Text 14 Mexico, Feb 14, 1975)

Devotee - "I want to know exactly what is the form of the body. If the spirit soul (jiva-soul) is non-material, what is the form?"

Srila Prabhupāda - "There is form, just like this material body is compared with the dress. Now, just like in your present material form you have got hand; therefore your coat has got hand, you have got leg; therefore your pant has got leg. Therefore, it is to be assumed that the spirit soul has got form, and it has developed into hands, legs, heads, everything. It is not formless; it has got form. But with our material eyes at the present, gross eyes, we cannot find it; therefore we say it has no form." (Lecture BG, Ch 2 text 14 Mexico, Feb 14, 1975)

Devotee - "Śrīla Prabhupāda, you state that spirit soul has form."

Srila Prabhupāda - "Yes."

Devotee - "Otherwise, how is the material body grown to accommodate the spirit soul? Just like a shirt has no form, but when it's put on the body, it takes the shapes of the body. Does that mean that the jiva-soul has the shape of the body that is accommodating it?"

Srila Prabhupāda - "Yes, you have got body, shape, very minute shape, that we cannot see, we cannot measure. Therefore in the Bhagavad-gītā it is said, anumeyam. You cannot measure. What is that word used? Aprameyam. Aprameyam, you cannot measure but it has a form. What is the length and breadth of that form, that is not in your power to understand, not materially. If you have got spiritual power then you can measure it. And that measurement is also given in the śāstra. What is that? One ten-thousandth part of the tip of the hair. Hair is a very small point. And divide it into ten thousand parts. That one part is the measure, magnitude of the soul." (Lecture SB, Canto 1 Ch 16 text 24 Hawaii, Jan 20, 1974)

The marginal living entities (jiva-souls) originate from Goloka-Vrindavana and NOT from the Impersonal Brahman or the Body of Maha-Visnu as Prabhupada teaches.

The eternal constitutional position of all jiva-souls are they are originally nitya-siddha because they all come from their infinite home Goloka-Vrindavana.

Only when the jiva-souls enter the material creation and the impersonal brahman do they then become eternally conditioned (nitya-baddha)

Therefore nitya-siddha can become a nitya-baddhas and nitya-baddhas can AGAIN become nitya-siddha.

No jiva-souls originate from the impersonal Brahmajyoti which is a condition of consciousness the jiva-souls fall too as Prabhupada explains here-

Srila Prabhupada - "Existence in the impersonal brahman is also within the category of non-Krsna consciousness. Those who are in the brahman effulgence are also in the fallen condition, so there is no question of falling down from a fallen condition. When fall takes place, it means falling down from the non-fallen condition. The non-fallen condition is Krsna consciousness." (Letter to Revatinandana, Los Angeles 13 June, 1970)

Acyutananda – "In the Bhagavad Gita it says, "Once coming there to the spiritual Abodes, he never returns to the material worlds, he can return?"

Srila Prabhupada – "If he likes he can return, that is voluntary."

Guru-kripa – "How is it that one can become envious of Krsna?"

Srila Prabhupada – "You have got little independence, you can violate. Because you are part and parcel of God, God has got full independence, but you have got little independence, proportionately, because you are part and parcel, if he likes, he can return. That independence has to be accepted, little independence. We can misuse that. Krsna-bahirmukha haïä bhoga väïchä kare. That misuse is the cause of our falldown." (Conversation, Mayapur, Feb 19, 1976)

So clearly those who believe no one can ever fall down from Vaikuntha have not understood the variety of living entities in Vaikuntha of whom the jiva-souls are just one and Prabhupada's comments here.

As said above, only a very small minority of marginal living entities jiva-souls (less than 10%) choose to leave.

Srila Prabhupada - "So everyone can know that independence means one can use it properly, one can misuse it. That is independence. If you make it one way only, that you cannot become fall down, that is not independence. That is force. Therefore Krsna says, yathecchasi tathä kuru. "Now you do whatever you like." (Los Angeles, June 23, 1975)

Srila Prabhupada - "Love is reciprocal, voluntary, good exchange of feeling, then there is love. Not by force! Krsna does not want to become a lover like that." (Washington DC July 8, 1976)

Srila Prabhupāda – "Unless there are "two-persons," where is the question of love? Love means two persons, then there is exchange, then there is love. I must deal with you open-hearted, you must deal with me open-hearted, then there is love. So if you want to love Kṛṣṇa, God, then these things must be there." (Aug 9, 1976, Tehran)**.