Joint and Several Liability

My question involves landlord-tenant law in the State of: Florida

My question is revolving around the topic of joint and several liability. Two tenants are on a lease, the first gives notice to the landlord that he is moving out and does so, the second does not.

My understanding of joint and several is that at this point, the second tenant would be liable for all of the rent? Both tenants signed the lease and were listed on the lease.

Is there any case law in Florida pertaining to this?

We're talking about what here - a month-to-month tenancy, with the first tenant giving the landlord full and proper notice that he intends to move out?