What is the ruling on purchasing an apartment by installments, given that the lessor stipulates taking rent for the previous period if the buyer defaults on payment?

The aforementioned transaction is invalid. If the sale contract was concluded and the buyer took possession of the apartment, then the contract was rescinded due to the buyer's inability to pay the installments or by stipulating a rescission option, the seller must return all received installments. The seller is not entitled to claim compensation for the buyer's occupancy of the apartment for the preceding period, because the apartment was not owned by the seller during that period. It is also impermissible to stipulate compensation in exchange for rescission. The usufruct (ghallah) belongs to the buyer until the time of rescission, because "profit follows responsibility (for loss)" (al-kharaj bi al-daman).