Wow. This sounds crazy. Alot of issues to deal with here. Let me try and break them down as they relate to a solution.
For starters, you will need to refer to your lease. These are your instructions for how to handle EVERYTHING! I can't, and won't speak to a Texas lease because I am in AZ, but I can speak to things that you need to look into as it should be the same.
First, are both tenants on the lease, and responsible for the lease? If so, then even if 1 roommate moves out and relinquishes, they are still liable for the lease. It's all about possession. IF they have told you they are out, but clearly haven't relinquished ALL keys, and haven't vacated, then they are still in possession, and you can collect rent for each day that they are in possession. IF they have given you all keys, and are out, but just left a bunch of stuff there, it is considered garbage/abandoned, and you can charge them for removing it. Again, full disclosure, I am speaking to AZ leases. So, you will want to refer to your lease for specifics on what it calls for. There is a section on possession. If you have to evict, and they leave stuff, you have to store it for 30 days before throwing it away, but you can charge them for the storage.
Regarding a Tenant at Sufferage (this is the Tenant that hasn't moved out yet), you have to go through the eviction process for this. Send your 5 day pay or quit ASAP to get this started. They will owe you for rent each day that they continue to stay beyond their lease expiration. Your agent may be correct in advising you that you can charge the whole month, but a judge may be more sympathetic and allow for a prorate of the rental rate. Therefore, you may want to look at a prorate when you file court docs to appear sympathetic yourself so that you have the judge on your side (they are supposed to be impartial, but they always seem to side with the "poor tenant who is being kicked out" instead of the "big bad mean landlord").
Now, regarding the funds you received from the auto-pay of their monthly rent. These are intended as rents, not deposits. If you refer to your lease, it will probably tell you that pre-paid rents (in this case they would be post-paid rents) cannot be used for damages or considered as security deposits. So, in my opinion (again, unless your lease in Texas states differently), you cannot keep these funds to cover damages unless you have written agreement from the Tenant to do so.
I know this isn't what you want to hear, but you will most likely have to return the post-paid rent, and then pursue an eviction to get the 2nd tenant out, and collect for damages. Most likely, when the Tenant figures out their auto pay went through, they will contact the bank and have it reversed anyway, so my guess is that money won't stay in your account long.
I hope this helps. Best of luck to you.