Is it permissible to take a loan from usurious banks out of material necessity, such as protection from imprisonment, given the impossibility of finding other alternatives after searching, and is this considered a legitimate excuse in Islamic law?

Borrowing with usury is one of the gravest sins and is only permissible in cases of genuine and compelling necessity, and only to the extent of that necessity. If someone is in debt and unable to repay it, the Islamic ruling is to grant them respite until Allah makes it easy for them to settle their debt. Imprisoning them while they are unable to pay is an injustice, based on the Almighty's saying: "And if there is one in [financial] hardship, then [let there be] postponement until [a time of] ease." If someone rejects a debtor's request for help in repaying their debt, they do not commit a sin, but they miss out on a great reward.