For a good summary of the rights of Texas employees when they lose their job, see Aaron Ramirez’ post from last March. Note that Aaron makes no mention of the employer paying the employee for any accrued vacation or sick leave. An at-will employee, which includes most employees in Texas, has no right to be paid for vacation and sick leave. You receive severance pay only if the employer expressly agrees to do so.
A terminated employee has the right to continue health insurance. But, you will have to pay the employer’s portion, wichh often makes the health insurance too expensive.