I found this information on a site I trust. I hope you find it helpful.
Call your local Department of Social Services, and somebody there should be able to tell you what is available in Texas. Also call your County Welfare Office. Be aware that some programs do have to be repaid. Some states do have a free dental service, that certain dentists volunteer to be part of. They will be called different things in different states. Where I live there is such a thing, but I don't know what it is called.
A friend of mine in another part of the state had really old dentures that broke and couldn't be repaired because they had got so thin. Anyway she got new dentures through this program. She had to drive 50-60 miles one way to obtain this service, and she had to make a few trips, but she said it was well worth it. Also I do see lots of seniors that have no teeth.
Found this listing in Google. Has lots of phone numbers to call. Hopefully this helps.
I am on SSI and I searched high and low for an answer to this and came up with denturesonline.com. How it works is they tell you how and you make the impressions, pick the color, fit a wax imprint to your bite, they make a wax sample with the teethon it for you to fit. You make any changes, then they make the final product and it costs $495 per upper and lower denture, and you can pay in payments with no additional charges. I'm doing mine thru them and it's all been really simple and if you have questions they help you and are patient and nice about it all. They do dentures for all over the USA.