Until such time as the landlord agrees to release a tenant from liability under the terms of a lease, the tenants listed in the lease are obligated together to abide by those terms (i.e. pay the rent).
Unilateral pronouncements by a tenant delivered to a landlord will usually not result in a termination of liability for that tenant.
However, in a divorce proceeding, the terms of the divorce (or settlement agreement) could address which spouse is obligated to pay the leasehold obligation (or some form of joint payment is a possibility as well).