In Jain Dharma, we have to see this from two angles – vyavahār naya (practical/outer view) and niścay naya (real/inner view).

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1. Mithyādṛṣṭi jīv (soul with wrong belief)

Can he take prāyaścitta (repentance / expiation)?

• Vyavahār (outer):

Yes. A mithyādṛṣṭi person can: - feel regret for a wrong act, - confess to guru, - do fasts, jāp, pratikramaṇ etc. All these are also called prāyaścitta at the practical level and they give puṇya and help in inner purification.

• Niścay (inner):

Real prāyaścitta means: - deep inner regret (ālokan, pratikramaṇ, pratyākhyān in true sense), - turning away from the fault with right understanding of self. This full, true prāyaścitta is complete only when there is samyagdarśan (right faith). A mithyādṛṣṭi has deluded vision, so: - his prāyaścitta is good and helpful, - but not of the highest spiritual level. It can become a step towards samyagdarśan in future.

After taking prāyaścitta, can he act on it?

• Yes, he can decide: “I will not repeat this sin,” and try to follow it.
• If he breaks it again:

- that is a new fault, - and if he had taken prāyaścitta insincerely, that itself becomes a serious lapse in truthfulness.

So, mithyādṛṣṭi jīv can take prāyaścitta and act on it, but the spiritual depth is limited by his wrong belief.

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2. Abhavi / Abhavya jīv (abhavya soul)

Who is abhavya?

• According to Jain philosophy, some souls are abhavya –

they will never attain moksha in the infinite future.

• This is a technical tattva point, not something we can label about any particular person easily in practice.

Can abhavya jīv take prāyaścitta?

• Yes, from vyavahār naya:

- He can do all outer forms of prāyaścitta – fasts, pratikramaṇ, confession, etc. - He can feel regret, improve conduct, do lots of puṇya. - These will give him better births, sukh, higher status etc.

• But due to his abhavya nature, that inner transformation will never reach the final state of keval jñān and moksha.

His prāyaścitta works only up to the level allowed by his bhavya/abhavya capacity.

After receiving prāyaścitta, can he act on it?

• Yes, he can follow vows, avoid faults, live a very disciplined life.
• The effect will be:

- reduction of certain paap, - gain of much puṇya, - but no final liberation.

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3. Summary in simple words

• Mithyādṛṣṭi jīv

- Can take prāyaścitta. - Can act on it and improve his life. - His prāyaścitta is good but not at the highest spiritual level until he gets samyagdarśan.

• Abhavya jīv

- Can also take prāyaścitta and live a very “religious” outer life. - Gets puṇya and better births, but never moksha. - His prāyaścitta does not lead to final liberation because his soul is incapable of moksha.

From the practical side, both can and do take prāyaścitta and act on it. From the ultimate spiritual side, only a bhavya soul with samyagdarśan can perform fully effective prāyaścitta that directly leads toward moksha.

If you want to see how this ties to stages of the soul (gunasthān), you can read more here