Severance pay without signed agreement

My husband was recently laid-off from his job. He was sent a legal agreement in the mail from the corporate office which sounded very "fishy" . The agreement said he would never seek future employment with the company. For this I am concerned. There is no reason that this clause should be in the agreement. This is a nation wide company with many different entities and there very well could be a time that a job at a different location might be appropriate. This company is based in Florida, although the agreement was sent from Dallas. There are many references to florida law included. Although the agreement has not been signed and returned, the company has sent severence pay. I am concerned that this document may have been forged, as my spouse was told of forged documents sent from his office to the head office in Dallas. What should we do? Is this legal to pay severance without the agreement signed? Should I be concerned at all? Thank you for your time.
NurseJ