Co-tenant's liability for lease renewal

The renewal lease is most certainly binding on the co-tenant who signs it;  whether the other co-tenant is also bound is less likely, and there would probably have to be something more than just having been co-tenants to that point to justify letting the first one's signature bind the second one.  The law would look at this as a question of whether the first tenant was an agent for the second one, and that agency relationship isn't something that can be assumed.

The liability for breaking the lease is potentially the rent, for the full term of the lease, or to the extent that the landlord can't collect that rent from a new tenant after a commercially reasonable attempt to re-rent.