no not really
Probate allows you to do deal with an estate ( and it costs)
if there is no estate ( or it is small - less than 5k ) then they may not bother. If the estate is insolvent then the person doing the clearing up (it doesnt even have to be an heir ) just writes a load of letters saying there is no money to pay this or that bill.
all this assumes when a person says there is no money then there is no money. ( and not s/t like - there is no money but there will be if you forgive the debt)
People think that if the dead man has assets of £500 and liabilities of £1000 - clearly insolvent then what happens is that you forgive (then get forgiven) the debts of £1000 and someone then pockets £500. You dont
You pay off the debts of £1000 in the order prescribed by law and write off what is left.
( I had relatives apply for the £250 from the sideboard which was the dead man's little float and I said no it was £2.50 because he drank as you well know and you dont want to contribute to the cost of his funeral do you no I thought not)