pudding:
standardly, it's up to the employer to decide when an employee is terminated once they are disabled. many employers decide to terminate an employee the day he or she is eligible for long-term disability. however, i've seen employers terminate employees the day of disability if it is an apparent long term claim or even after one or two months. now, as far as texas goes, i'm not aware of any law mandating when an employer can or can not terminate a disabled employee. i've never heard of any in any other state as well, but my expertise on this subject would only be limited to a handful of states.
as far as being denied information on your ltd plan, that's a whole separat issue you need to take up with your employer. if you are terminated and are worried about medical insurance since you mentioned you have diabetes, then COBRA the medical.