Yes, it is legal to require a tenant or prospective tenant to provide a SSN for purposes of security check; renting an apartment to someone is a voluntary act (landlords don't have to be landlords; they choose to enter that  business and provide that service), and so landlords may require various background or credit checks.However, if the finance is not a prospective tenant but rather is a guest  of your daughter, who is the tenant, then the landlord only has whatever authority or power over guests as the lease itself grants it.  If there are any provisions or clauses in the lease which allow the landlord to exclude guests, limit their stays, ask them to leave, etc., those provisions are usually legal and enforceable...however, in the absence of some such term in the lease, the landlord would seem to have no authority over who your daughter has a guest, when.