The simple answer is no. The debts you run up during your lifetime don’t automatically transfer to your heirs when you pass away. Generally, they fall to your estate. Your personal representative must pay your debts from the estate’s assets before distributing anything to your heirs.
Often, collection agencies make the surviving spouse feel as if it’s their responsibility to pay off their loved one’s debt. But that’s generally not the case.
That said, there are some exceptions. Some types of debt pass directly to someone else when you die. For example, say you share a joint credit card account with your spouse. Usually, on your death your spouse becomes solely responsible for any amount owing on the account. Another example: if someone co-signed a loan for you, the creditor could demand payment from them if you pass away with the loan still outstanding.