No roommate agreement. One roommates wants to move out early of 1 year lease. Who pays rent?

Who pays rent?

It entirely depends on the terms of the lease the co-tenants jointly signed. It is impossible to address your question with specificity or certainty unless we know the terms of the lease.

For instance, if the lease mentions that co-tenants are jointly and severally liable, then the landlord is entitled to recover from any co-tenant any and all fees pursuant to the lease. In that case it would not matter who left prematurely or why. Absent a roommate agreement, the payer might in turn have a claim on equitable grounds, on a theory of implied contract, or quasi-contract against the co-tenant who left prematurely, although that is a separate matter and does not alter the landlord's entitlement to obtain full recovery from any co-tenant.