Absolutely. If they didn't give notice they were moving you can charge as your lease allows (usually 30 day notice) so depending on when they moved out, it might be 2 months rent. You can also charge for cleaning, hauling of the junk, and any other damage they may have done.
Often times the security deposit won't cover it all. Send them a bill, but it's unlikely they will pay. You can take them to small claims court and get a judgement but in Texas you can't garnish wages so it is not worth a lot. You can just report it to the credit beauro through a service on this site which I would recommend.They may want to buy a house one day and that will prevent the loan from going through then they will be back wanting to pay you off.
I always tell my tenants that unlike other states, Texas laws are written such that I can not wait to file for eviction as there is no provisions for equitable recovery. I will file on the 5th if rent is not paid period. It takes about 3 weeks to go through the eviction process so that helps limit losses to 1 month rent.
The other thing you should consider is how you got to this point. It's often difficult to look in the mirror but ask yourself what you could have done differently to avoid a tenant like this in the future. There are many applicant qualification techniques that help including credit checks, past landlord references, and in-home inspection of where they are living now as a few examples. The goal when you have a problem should be to improve your processes to eliminate that failure point moving forward.
--209.205.xxx.xx