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I'm sorry to hear about your situation. Florida (like all states) has a Medicaid "recovery" law. You can find that law here: http://www.flsenate.gov/Laws/Statutes/2012/409.9101
Under Florida probate law, some estate assets may be exempt or protected from creditors who have filed claims against the estate. The probate judge makes the determination about what is exempt. In general, if the Medicaid recipient owned the home as the primary place of residence and it passes to the decedent’s relatives, the judge would likely declare it to be "homestead protected from creditors." If so, then Medicaid, or any other creditor, cannot force its sale. If however, any real property is not "homestead protected," it may need to be sold to pay Medicaid.
If you're not living in the house and there are no other exceptions apply (not under 21, not permanently disabled or blind) then Medicaid would have a claim against the assets of your father at the time of his death for repayment. Note that this does not necessarily mean that they will take his house. That all depends upon the "debt" that would need to be repaid. But assuming that they have spent a significant sum for his care, it's far more likely that they would recapture his home than not as part of the recovery process.
Note that they won't take possession while he's alive. It's a recovery against the estate. So the answer to your specific question is "neither", in that they won't take it while he's alive AND you would not inherit the house.
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!