Employment Law Questions? Ask an Employment Lawyer.
I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your dilemma.
You'd still be considered to be quitting if you were to leave your new job during the probationary period. If they choose not to hire you based on something that is not your fault, then you can go back and reopen your claim for benefits going forward. But because one of the requirements of receiving benefits is that you accept work if it is offered, you will lose your benefits if you leave the new job without just cause - something like they're asking you to do something illegal. You might not lose full benefits if the job is only part time (depending on the pay and how much you're getting), but you could lose a good chunk of them.
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