Yes, they do indeed. I had to prove my mum lived on disabled benefits, in a council property and left absolutely nothing to anyone when she died, I had to provide evidence there was nothing in any bank accounts, even old ones going back years. I kept her debt free but it was just her last few bills that there was nothing to pay them with. Don't let anyone fool you that your debts die with you, they don't.
If you can prove they have nothing, any company can only ask the next of kin to pay once, if they say no as they've got nothing either, the companies aren't allowed to ask again