Job offer dilemma

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Hello

I would like to describe my situation before I get to the questions.

Let's start from the beginning. Some time ago I quit my nursing assistant job(LTC) without a proper notice.(death of a family member,I had to leave USA in the next 48 hours after it happened). It makes me not rehire-able.

I came back and I have been looking for a job since. I have two job offers already. Different hospitals,different units. Let's call them hospital "X" and "Y". Here is my problem:

Hospital X(Rehab) knows that I am not rehireable and is ok with that. They scheduled an orientation/drug test already.

Hospital Y(SICU) doesn't know the situation with my last employer,and still wants to hire me. They scheduled an orientation date/ drug test as well.

So do you guys know if hospital "Y" can turn me down if the job offer was made and I accepted it? Do you think it's good idea to let HR know about what happened with my last employer or should I just keep my mouse shoot since they already offered me a job? So I am kinda confused here if you have any experience or opinion please let me know.

Thank you

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