Can an employer lay an employee off while the employee is on long-term disability?

Yes.  The only law in North Caroilna that protects your job while you are unable to work is the FMLA (or rare cases the ADA).  If you were FMLA eligible, the employer would have been required to keep you employed for 12 weeks.  If you were unable to return with in 12 weeks, then the employer would be legally required to return you to the same or a substantially similiar job.  However, if you were unable to return, then you could be legally terminated at 12 weeks and 1 day. As such, if you went out of work on March 31st, then you ran out of FMLA on or about June 23rd.  The ADA might, in some circumstances, require an employer to provide you with a short amount of time away beyond FMLA.  However, it does not sound like this applies in your case based on the information you provided.