Is the money that the daughter received in exchange for waiving her claim to the apartment, which was rented to her father, considered permissible for the heirs to inherit?

If the apartment is rented from the state or the Awqaf (Endowments), then the old, perpetual lease contract is Islamically invalid due to the unknown duration. The contract must be فسخ (annulled), and the property returned to the owner without compensation, with the tenant paying the fair market rent for the period of their use. If the apartment owner paid "khuluw" (eviction compensation) to the tenant without the owner's willingness in order to vacate their apartment, then this money is not permissible for the tenant, and they must return it to its owner or seek their forgiveness; otherwise, they are consuming money unjustly, as Allah Almighty says: "O you who have believed, do not consume one another's wealth unjustly but only [in lawful] trade by mutual consent." Similarly, it is not permissible for the heirs, and they must deduct it from the inheritance before distribution.