Is it permissible to take a sum of money from a new tenant in exchange for vacating the dwelling, especially if the contract with the owner is open-ended, and is the tenant sinful for paying this amount when there is an urgent need for housing?

If a tenant waives his right to the lease term in favor of another tenant in exchange for a sum of money, this is a permissible "khalw" (key money), because transferring rights for compensation is legitimate according to some scholars. This is called "al-faragh wal-ifragh," which is the waiver of a right, such as waiving the "khalw" by its owner to another in exchange for compensation. It is also permissible to sell furniture for a sum of money, as this is the sale of a owned physical asset.