Is it permissible to take out an interest-bearing loan to avoid imprisonment due to inability to pay debts?

The answer to your question is that if you are unable to acquire money through permissible, lawful means, and your inability to pay the amount will result in imprisonment, then it is hoped that you will be considered among those compelled to engage in usurious dealings, and there will be no sin upon you. The sin is upon the one who lends with interest, and upon whoever knew of your situation but did not help you despite being able to. Remember that necessity is determined by its extent; thus, it is impermissible to take more than what protects you from harm. You must hasten to repay the debt if you find money, in order to free yourself from the usurious interest.