When you pass away, your estate is still obligated to pay any debts you have and to fulfill any contracts you have signed, if possible. You cannot expect to escape your credit card debts, for example, by dying.
However, some things are not as simple.
What if you have signed a rental agreement as a co-lessor with a roommate? Ordinarily, if you do not pay the rent while you are alive, then the landlord can sue either roommate individually for the total amount owed or both jointly. If you pass away, the roommate is still responsible for the total amount of the lease, but can that roommate sue your estate for the amount you still owe under the lease?
That is essentially the question someone asked the New York Times recently in "A Roommate Dies; Must His Estate Pay the Rent?"
In this case, a woman was renting a garage apartment with her boyfriend who passed away. She continued to pay the full rent and wondered if she could receive her boyfriend's share of the rent from his estate.
The simple answer is yes, she can.
The estate, if it has the money to do so, would normally be responsible to pay her back for the rent. However, her claim against the estate would come after any tax liabilities or secured creditors and she would only get paid, if there is enough money left in the estate to do so.
Her position could be strengthened if she and her boyfriend had signed a written agreement about the amount of rent each of them was responsible for and what to do in the event one of them passed away during the term of the lease.
Reference: New York Times (Nov. 5, 2016) "A Roommate Dies; Must His Estate Pay the Rent?"