Is it permissible to give the female partner, to whom the donation was made, the agreed-upon amount of (8000) riyals from her capital of (6000) riyals, even though the project has incurred a loss?

Among the conditions for a valid Mudarabah (profit-sharing) contract are the agreement of both parties on a common percentage of the profit and the non-guarantee of the worker against loss. If they do not agree on the profit percentage or if a guarantee is stipulated for the worker, the Mudarabah is invalid. In such a case, the owner of the capital is entitled to all the profit, and the worker is entitled to a fair wage (Ajrat Mithl), according to the majority of scholars. As for the loss, it is borne entirely by the owner of the capital, and the worker is entitled to a fair wage. In this scenario, the contract is invalid due to the lack of agreement on the profit distribution ratio. The mother of the questioner's commitment to return the principal or more than it, if it is a donation from her and not a condition in the contract, then there is no harm in it. Your mother is obligated to return the remaining principal if she did not act negligently or exceed her authority, and anything beyond that is considered a donation from her.