Is it permissible to sell company assets at a loss if there is no liquidity to end the partnership, and is what the departing partner demands—obtaining his full share of the rent in addition to his profit—considered an injustice to him?

If the sale is at a loss, with the partner's knowledge and request, then there is no injustice to him. The same applies if he requests to receive his share in installments. Injustice occurs when there is a delay in paying a debt despite being able to, as the Prophet, peace and blessings be upon him, said: "The delay in payment by a rich person is injustice." However, if one is unable, Allah does not burden a soul beyond its capacity, and it is obligatory to grant respite until a time of ease.