There are two things ~ Convention and law. While almost all companies may follow a convention of not recruiting back an absconded person for obvious reasons, the law does not deny the opportunity to the person per se. The answer to your question, therefore, is ~ Yes, technically, a person IS ELIGIBLE to apply for a position to an organization where he / she worked in the past, but did not separate following (internal) process. If the act of absconding invited legal action (pending with the organization), beware, you will play into the hands of the organization to re-open the case!
All said and done, at the outset, try to always separate clean. No organization is that cruel to force anyone to take the extreme step. Remember that "Organization is always bigger than the individual".
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