In Texas, if you do not leave a will, the creditors cannot collect from family members. If you do leave a will, naming an executor, they most definitely will go after family members. Then the whole "get a letter, the estate is broke" thing comes in to play.
Happened to one of my co-workers when his mother passed away leaving no will, the only reason I have this tidbit of trivia.
I’m not an estate lawyer (though I am an attorney in Texas), but ...
If there is no executor/will, I think creditors can drive the estate into probate court and have an executor forcibly assigned. Just because there is no will does not mean the family can bolt with money/assets without paying the debts from that money/assets. If someone has a $50K estate, $25K in debt, and no will ... the inheritance would be done through probate court, after the debts are paid.
SnakeDoc