What is the ruling on paying off the accumulated debts of a deceased person by someone who is not a relative, and is he obliged to continue doing so despite his fear of not being able to fulfill it in the future, and what are the other ways to pay off the debt?

Paying off the debt of the deceased - especially if they did not leave behind enough to cover it - is a form of kindness to them, as per the Hadith: "The soul of the Son of Adam remains suspended by his debt until it is paid off," meaning it is held back and detained. However, the deceased's accountability is hoped to be cleared by the intention and determination to pay off the debt, as per the Hadith: "Whoever takes people's money with the intention of repaying it, Allah will repay it for him." Your repayment of the deceased's debt is a kindness to them, and you will be rewarded for it. If you find something more deserving of financial precedence, then there is no blame upon you for not repaying their debt.