They don’t at least in most of the western world you can’t inherit debt. It all comes out of the estate and if the estate isn’t worth enough then the lenders are out of luck. Now that doesn’t mean that unscrupulous lenders won’t try to go after the family but legally they don’t have a leg to stand on as long as you don’t start paying them. At least in the US if you pay them anything then they can take that to court as you agreeing to pick up the debt but if you just tell them to go pound sand then they can’t do anything.