No one. A lot of loans, such as student loans, are forgiven when someone dies, as stated in the original loan agreement. In the event of a car payment or house payment, the lender is entitled to claim the property, which was put up as collateral for the loan to begin with. As for other payments, the lender is out of luck. They are not entitled to chase after people who did not sign onto the loan. If they have no property to claim, they take the loss and pass the difference on to other customers in the form of higher interest rates, so the loss does not eat into their profits. They assume this will happen to a certain number of loans, and build it into their metrics every year.

As they say, you can't get blood from a turnip, and you can't get loan payments from a corpse.

It is important to know when you're co-signing for any loans what would happen in the event that the primary account holder were to pass away. It's also important to know which loans can pursue claims against your estate following your death, in the event that you do have heirs.

If the person has absolutely no heirs, the inheritance goes to the state which then settles the inheritance. This includes paying off outstanding debt. The remaining amount is kept by the state. This is called escheat. Under common law, property is never left without an owner; unclaimed property always goes to the state.
Different states have different procedures on handling creditors with claims on estates that have escheated. For example in Virginia the creditor needs to petition the court with an affidavit attesting to the fact that the debt is due.

When you die intestate the State will take over the property. The State when it escheats your property has two obligations. To look for a rightful heir by posting so in the newspaper. In addition the Stae will post in the newwspaper that they have taken possession of your estate and all claims against it need to be filed. You have a year to file your claim. If you have a mortgage they will run to file first to claim the house. Depending on the balance to the value the State will release it to them or sell it and pay them off. Car loans will result in a returned vehicle. Other contracted debts loans, credit cards and private debt will be paid off. Unsecured loans will be filed but are not likely to be paid unless there is some type of proof that would show this was a normal and usual transaction. What's left goes to the State and any shortage of funds are released in the above order in a first come first served basis.