The debts very much don't die with the person - the estate is on the hook to pay your debts before distributing to heirs.
Obviously, with some "it depends" nuance - but if the difference between this and your world view would make a significant difference to your loved ones, you might want to talk to an attorney.
Correct, but if you die broke, nobody else is on the hook to pay your debts, unless that person cosigned a loan or something like that.