Am I sinful if I fail to pay a debt tied to training that qualifies me to work in an institution that commits unlawful acts, and is it permissible for me to remain in this institution until I am able to repay the amount owed, especially if I am threatened with imprisonment or legal prosecution?

If the questioner has committed himself to permissible work, and the company obliges him to perform forbidden work, then he is not permitted to fulfill their desire. He may submit his resignation without being obligated to pay expenses, because he has fulfilled his condition. As for their condition of performing forbidden work, it is a void condition, based on the saying of the Prophet, peace and blessings be upon him: "What is wrong with people who stipulate conditions that are not in the Book of Allah? Whoever stipulates a condition that is not in the Book of Allah, it is void, even if it were a hundred conditions. The Book of Allah is more deserving, and the conditions of Allah are more binding." However, if the questioner knows that he will be subjected to imprisonment, he may remain in the work to the extent that he obtains his fees.