Is it permissible for me to ask a well-off creditor to forgive the debt I owe him, given that I cannot find work to repay it?

If the debt is due and you are able to repay it, then it is obligatory upon you to do so. However, if you are unable to repay it, there is no blame upon you for its delay, due to Allah's saying: "So fear Allah as much as you are able," and His saying: "Allah does not burden a soul beyond its capacity," and due to the Prophet's (peace be upon him) saying: "The procrastination of the rich is injustice."