Is taking money from others to pay profits, in the hope of gain after a previous loss, while the debtor owns nothing but his home, considered usury, and what is the way out of this situation?

The Mudarib (agent in a Mudarabah (definition) contract) does not guarantee the principal capital nor does he bear the loss, unless there is a transgression or negligence on his part. Therefore, the capital owners have no right to demand it from him or to demand an increase on it. However, if you took money from others to give profits to those who are demanding them from you, then this is an invalid action and an infringement upon their money, which they paid for Mudarabah, not to جبر (compensate for) a previous loss. If you guaranteed them those funds, then it is Riba (usury). Otherwise, it is an infringement that makes you liable for their money.