What is the ruling on a family lying to the rental agency that the sister who is the tenant resides in the house, so they can avoid eviction from it, while they know that the sister rents out the house for illicit activities and claims to live in it to obtain welfare benefits from social services?

The default rule is that a tenant may allow others to reside in the rented property, provided that it does not increase damage to the property. However, scholars differed on this point if the landlord stipulated that no one else should reside there:

Hanafi school: The condition is void, and the contract is valid. The tenant may allow others to reside there. Maliki and Hanbali schools: The condition is valid, and the tenant may not allow others to reside there, except as dictated by custom. This is the preferred view. Shafi'i school: Both the condition and the contract are void.

Based on this, the tenant is not permitted to allow others to reside there, in adherence to the landlord's condition. Furthermore, it is not permissible to lie to the institution, because lying is forbidden unless there is a necessity and a benefit.