why couldn't you (as the inheritee?) "throw away" all assets prior to dying, then let your benifactors refuse the debts (which is all that's left)? Who actually enforces that you can't dispose of your assets (in a way that benefits your son/daughter/spouse), then refuse the debt?
Whenever you take a loan for your house, a bank will want to add a note to the registry that it has first claim to your property in case of not paying, premature death, and so on. So one cannot just give his house to his relatives, as the court will block the transfer when it will see in the registry that the bank has primary claim to it. To do something like that, one must make a deal with the bank that new owner will either pay up the loan or take it on his name.
[1]http://en.wikipedia.org/wiki/Gift_tax_in_the_United_States#N...
Though in the case of a mortgage, losing the debt also means losing the house. I totally understand wanting your family to be able to keep the house. Losing your dad/husband and also having to leave the house with all the memories of him, would suck double.