Am I responsible for the debt of a person who has named me as being responsible for their estate when they pass.

Where you write “named me as being responsible for their estate”, I gather that the maker of the will has nominated you to administer the will as the executor or personal representative.

You are certainly free to decline that position. However, since you are talking in future tense “when they pass” you should promptly inform the individual, before he or she passes, that you do not wish to assume that responsibility.

Whatever, you are not going to be liable for any debts simply by virtue of being named and/or appointed the personal representative of the estate.