Maybe. Severance is not required in Texas (or in 46 other states, and is only required in extremely limited circumstances in the three remaining). So the question is going to be whether or not the company's policy constitutes a binding contract. It is my understanding that Texas does not look at past policy when determining contract issues, so you will need to show that the company had a contract with YOU to provide you with severance. (I'm not saying that a statement in a company handbook can't be used to show that - only that their having paid other, previous employees cannot. That is, if my understanding of Texas regs is correct.)

Show any documentation you have that discusses the severance agreement to a local contract attorney and see what he/she says.