Given that the open enrollment period designed to allow U.S. citizens to take advantage of insurance premium subsidy savings in the healthcare marketplace ended in December 2017, you have fewer options. That said, you might still qualify for several programs:
If you're currently struggling financially and have a disability, you may qualify for Medicaid through the state. You can apply for that coverage at any time. The Texas Health and Human Services Medicaid and CHIP page has more information. If you experience a significant life event at any time, you may qualify to enroll under a "Special Enrollment" period rule. You can find more information about this option on HealthCare.gov. Life events that trigger a special enrollment include a move to or from Texas or a different county within the state, marriage, divorce, a new baby, adoption, losing coverage under your parents' plan, losing coverage from an employer, the start or end of AmeriCorps VISTA service, prison release and new citizenship. You can find the complete list of qualifying events for special enrollment here. You also qualify for a special enrollment if your health insurer pulled out of the marketplace within the last 60 days.
Of course, many insurers don't stop offering health insurance once the enrollment period ends. The biggest problem is cost. You will pay a higher premium amount without the premium subsidy discount offered during open enrollment. You will also probably have difficulty finding the same level of insurance coverage that you've enjoyed in the past at an affordable cost. Keep in mind that if you don't have any health insurance in 2018, the Internal Revenue Service can also still penalize you under the individual mandate rules of the Affordable Care Act. Although the tax bill signed into law in December 2017 removed the penalty, this aspect of the bill doesn't go into effect until 2019.