CHAPTER: If A Person Dies Owing Fasts, His Heir Should Fast On His Behalf.
Narrated Ibn Abbas: A woman came to the Prophet صلی اللہ علیہ وسلم and said (to him) that one month's fast was due from her mother who had died. May I fulfill them on her behalf? He asked: Suppose some debt was due from your mother, would you pay it ? She replied: Yes. He said: So the debt due to Allah is the one which most deserves to be paid.
Narrated Aishah: The Prophet صلی اللہ علیہ وسلم as saying: If anyone dies when some fast due from him has been unfulfilled, his heir must fast on his behalf.