OK, first I think you are referring to Medicaid, not Medicare. It is a common mistake, but they are different programs in every respect.
Secondly, Medicaid has the right to recover against property in a succession if the deceased person received Medicaid benefits prior to death. In almost all cases that would be nursing home care.
The right to recovery is against whatever interest the deceased person who received benefits had. So, the answer to your question is yes in some respects and no in others.
So, the problem is that a claim against a partial interest in a home effectively kills good title and interferes with everyone’s interest. Does that make sense?
On the other hand, if Medicaid did not actually pay out money for the care of the deceased, then they would have not claims against anyone.