If there were two or more co-tenants who entered into the contract, then unless they get the landlord's clear consent or are otherwise allowed by a Member of the Landlord and Tenant Board, they are both bound to the terms of the contract even if they no longer live in the property.
The landlord must still name both or all parties on the N4 for nonpayment or any other notices or applications, so that it is clear that the contract is still in full effect. The landlord may be able to apply for collection against either or both parties for garnishment, for example, at some future date.
Trying to make the tenant who left actually pay the rent or damages is not an easy thing to do, but the possibility of eviction because of this nonpayment usually acts as an incentive for whoever is still living in the property.