If said tenants stop paying rent you will only be able to take the person on the lease to court for non-payment of rent. The girlfriend will not be required by law to leave the apartment after eviction and the landlord will have to take her to court seperately in order to reclaim the apartment. It is in the best interest of the landlord to have all persons living in the apartment on the lease. In this case it does not seem a matter of doing background and credit checks, just a case of having all the t's crossed and i's dotted in case of the worst.
2001 A6 2.7t 6M - always a work in progress