The estate of the deceased is the only entity that is liable, to the extent of its assets. If there are assets left over, they will be divided equally among the beneficiaries. If not, the creditors get to write it off. That is an over simplified explanation, of course it can be more complicated. There are many other factors that affect the rights of the beneficiaries.

A simpler way to put this is; if there is an estate, all bills will be paid from that before any inheritance is given. The funeral costs will also come out of the estate. If the person has no money when they die their bills like credit cards, etc. are discharged and no one has to pay them. If there are Mortgages and the like the item will be reposessed or auctioned, and the funeral expenses will be the responsibility of the next of kin. If there is an estate after all bills are paid, each person, by law who could prove they were a legal heir would get an equal amount

If the bills are not in your name, then you are not responsible. But if you are living in the house then it is evident that you would want to continue to pay those bills, like lights and gas, etc. Just keep a record.
Do not pay any medical bills or other debts. They are no one’s responsibility if they are not in your name. Once an attorney has been contacted they will notify any creditors and they will have a certain amount of time to make a claim. If you all decide to keep the estate and not abandon it, then you will have to pay those creditors if they do indeed make a claim. But then and only then, do you have to pay any other debts of the deceased.