This question is just out of curiousity. Debt after one pes away?

My mom has a trust fund for me for 10000.00. It has her name and my name on it. Lets say she has a lot of debt and she pes away. Could the people she owe money too take money from the trust fund and would I be responsible for paying for her estate. And what about if I was her next of kin? How would this all work?