If, in the future, my ex dies and his mother is no longer alive, would my daughter be financially responsible for his debt?

Hello, The age of majority in Delaware is 19. While she is a minor she would not & could not be liable for any debts. When she reaches the age of majority and unless she co-signs or makes a writing of her intent to take on his debts -- she should not be liable. There are states that have so-called "filial responsibility laws". These laws allow nursing homes to seek reimbursement from the residents' children. Delaware is one of the states that has this law. So if your ex wound up in a nursing home, this may be an issue. I have attached an article that further describes "filial responsibility laws". Good luck.