Is it permissible to place a financial deposit in a bank for the purpose of renting a safe-deposit box to store valuable possessions, knowing that the bank stipulates this to guarantee its rights, and there is a fear of falling into usury?

If the deposit is guaranteed in exchange for profit, then it is a forbidden usurious transaction, and it is not permissible to engage in it. The need to preserve wealth does not justify entering into a forbidden contract, if it is possible to deal with an Islamic bank or deposit the money with a trustworthy person.