Is it permissible to demand the debt that represents half of the capital after the partner disposed of the shop by selling it without permission, and the project incurred losses?

You may pay the entire capital of the partnership and agree with your partner that half of the capital will be a debt upon him, which he will repay from his own money. However, if the two partners stipulate that the repayment be solely from the profits, then this is a void condition. In the event of a loss, your partner must return to you the entire capital you lent him. In a partnership, losses are distributed proportionally to the capital invested. So, if two individuals partner with equal capital, the loss is divided equally between them. As for Mudarabah (profit-sharing partnership), the loss in it is borne by the owner of the capital.