If the owner executes a Transfer of Death Instrument and property transfers to the beneficiary, does the beneficiary need to pay the medical bills?

The new owner has no liability for the medical expenses. It is as if there was a bank account with a TOD. The transferee has no liability to pay the bills of the deceased.

Assuming the Transfer on Death deed was properly executed and recorded in accord with Illinois statute, and the owner had the legal capacity to execute the deed, then the transfer is not subject to creditor or medical claims unless it was a fraudulent transfer. That means the transfer on death deed cannot be executed to avoid paying debts to creditors. The deed should be executed before any such debts are incurred. To accept the transfer, the beneficiary must file a statutory notice of death affidavit and acceptance within two years or the property reverts back to the owner's estate.