Firstly, sorry for your loss.
As there is no estate and if these debts are in your mothers name only, then no the debts do not pass on to the next of kin, no matter what the credit companies try and tell you. It does become more complicated if any of the debts are jointly owned.
If there was any money in the estate then the debts would need to be paid first before any beneficiaries received anything.
I am pretty sure I have that all correct, but there are other here who are much more knowledgably than me so hopefully they will put you straight if I am wrong.