Is it permissible to take a sum of money from the occupants of a rented apartment (old tenancy contract) in exchange for vacating it, in order to use it to complete the construction of a new, unfinished house, knowing that vacating the apartment means having no alternative shelter until the house is completed?

The tenant does not have the right to compel the landlord to pay money in exchange for vacating the leased property. The leased property belongs to the landlord, who has the right to dispose of it. If the lease duration is not specified (month-to-month), then either party may terminate the contract at any time. If the tenant prevents the landlord from reclaiming the apartment after it has been requested, then the tenant is responsible for guaranteeing a fair market rent to the landlord.