deceased renter

What is the name of your state?
New Mexico.
My aunt passed away and there is no probate. Her landlord held a deposit of $250 (which was to be returned after 3 years, but was not). The landlord has now submitted a bill to the "Administrator of the last will and test" of her estate for an additional $600 for cleaning, reupholtering a chair, pro-rated replacement of carpet, and missing items," etc. Since there is no probate, and she was not survived by a spouse or children, is there an obligation of anyone to pay the bill?

If the aunt has any assets left over, then it is the responsibility of the executor/administrator of her estate to get this bill paid. Someone of course would need to file to be administrator. If there are no other assets, then unfortunately the landlord will have to remain unpaid after deducting the deposit from the final bill.