Lease

There are three different ways to consider this question.

The first is a pure common-sense approach. You say, for example, that it is "obvious they are moving." Well, is that your guess, or have you asked them? COMMUNICATE with your tenant. They may be worried that you're completely unreasonable and inflexible. Some landlords are unreasonable and inflexible, but that's bad for business in the long run. So take the initiative. See what their plans are. Encourage them to confide in you and to be honest with you by pointing out that you'd like to avoid any kind of legal conflict with them -- and that SHOULD be true, because you're unlikely to do as well in court as you probably could via a reasonable agreement reached through open, good-faith negotiation.

Second: Re-read the lease. I'm guessing that you probably used a written lease form prepared by someone else or copied or borrowed from some group or association. Most leases contain language specifying the landlord's and tenant's respective rights and obligations, including such things as what kind of notice of default must be given, how long a cure period is allowed, and what happens if the tenant vacates before the lease term has expired. (If you didn't require the tenant to sign a written lease agreement when you leased the property, then you're going to suffer now for that, and that should be your first lesson from this experience.)

Third: There's a very specific body of landlord-tenant law, most of it contained in a series of statutes that are pretty straight-forward. Most of it is in Title 8 of the Texas Property Code, which comprises Chapters 91-94, which I'm linking below. It provides for the "default rules" on a lot of matters if the lease terms have not changed the default rules. You may be able to chart your path just by reading those. If, after you've tried communicating with the tenant and reviewing your lease, you still can't chart your path through them, perhaps you can return with a more specific question then.

Neither I nor any other lawyer can walk you through ALL the possible permutations of what you ought to do next at every point of the way without knowing what's in your lease (if you have a written lease) and more background details. In all probability, though, you're going to want to start by giving formal written notice to the tenant pointing out that he's in monetary default on the lease for nonpayment and demanding that he cure that default by making payment. I'd take that with you when you first go to talk with the tenant, and deliver it in person while you're trying to find out what's going on. (I'd also send copies by both regular and certified mail, return receipt requested, if you have any trouble meeting with him face to face and getting him to sign a copy of the notice to acknowledge receipt.) Pretty much all of your potential remedies begin with that sort of notice.

Oops. Forgot the link. Here it is: