Answering in simple terms, based fully on Jain siddhānt:

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1. Can abhavya / abhavi jīv take dīkshā?

Yes.

“Abhavya” (or abhavi jīv) means: a soul that will never attain moksha, because true samyak darshan (right faith) will never arise in it.

But such a soul can still:

• be born as a human,
• feel some dispassion,
• join sangh,
• formally take dīkshā,
• do tapas, jap, pāth, etc.

So from the outside, an abhavya jīv can become a monk / nun and live as a sadhu-sadhvī in the worldly sense (vyavahār naya). What will not happen is: the inner, real path leading to moksha (true samyak darshan, keval jñān, etc.).

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2. Can an abhavya jīv get vairāgya?

Yes, but with a limitation:

• They can feel temporary or partial vairāgya – disgust for worldly pleasures, attraction towards ascetic life, liking for solitude, etc.
• But they never get that deep, turning-point type of nishchay vairāgya which arises together with samyak darshan and leads eventually to moksha.

So:

• Outer vairāgya (leaving home, simple life, tapa) – possible.
• Inner, moksha-producing vairāgya – not possible for an abhavya jīv.

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3. Then what causes an abhavya jīv to take dīkshā?

Main causes (all due to its own puṇya and previous habits):

• Powerful puṇya karmas giving birth in good Jain family, near saints, etc.
• Influence of satsang and seeing peace of sādhus / sādhuīs.
• Fear of suffering, old age, death, hell, etc.
• Liking for respect, status, or comfort of monastic life (this can also be a subtle reason).
• Strong habit from past lives of doing religious activity.

All this can push even an abhavya soul to:

• feel, “Gṛihasth life is painful, I will renounce,”
• and actually take dīkshā and follow rules to a good extent.

But: Because of extremely strong mithyātva and anantānubandhi kaṣāyas that never get destroyed, true samyak darshan never arises, so real moksha-mārga never opens.

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4. Digambar / Śvetāmbara view

• Both accept Bhavya–Abhavya classification.
• Both agree:

- Abhavya = no moksha, no true samyak darshan, ever. - Only a Kevalī Bhagwān truly knows who is bhavya or abhavya.

• Practically, both traditions say:

- Never label anyone (including yourself) as abhavya. - Always live and strive as if you are bhavya.

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5. Practical takeaway for you

• Yes, abhavya jīv can take dīkshā and feel some vairāgya.
• But we are not Kevalī; we must never assume “I am abhavya so dīkshā or sādhanā is useless.”
• Jain dharma’s message is:

- Treat yourself as bhavya, - strengthen shraddhā, jñān, chāritra, - and reduce anger, pride, deceit, greed.

You can read a simple explanation of bhavya–abhavya jīv here