Some landlords make the mistake of splitting a $1000 monthly rent so that each tenant is responsible for $500—and accepting that amount from each tenant, month after month. When one tenant leaves, they worry about finding another tenant so that the remaining one can continue paying their $500.
However, the tenants are together responsible for ensuring the rent is paid in full; therefore, when one tenant moves out, the remaining tenant or tenants must continue paying the full rent on time every month. For example, if the lease runs through September and a tenant moves out in June, both tenants are still responsible for full rent until the end of September—whether that means the tenant who moved keeps paying their half on a rental they no longer live in, or the remaining tenant pays the entire rent.
In most cases, the lease will be in the names of each tenant, and each tenant is responsible for upholding its terms—including whatever penalties are in place for breaking the lease early. It is up to the tenants to work out how the full rent will be paid until the end of the lease.
Another issue some tenants raise is the security deposit. Would a tenant who is leaving early be entitled to a pro-rated portion of the security deposit they paid at move-in? Most landlords would say “no way.” It is standard practice to tie the security deposit to the rental unit. Only the tenants still living in the unit at the end of the lease would be eligible for any return of the security deposit.
Remember, if your tenant finds a new roommate, follow your standard procedures for any new tenant. This should include a lease application, thorough tenant screening and credit check, and checking all work and former rental references.