Typically among the issues that arise after employment ends are whether there is any severance package, whether any monies are due the employee, whether the employee will be eligible for unemployment insurance, and what sort of reference the employer will give the employee. If there was a non-compete agreement in effect, that, of course, can generate additional issues.
There is no requirement that there be any letter (or any agreement) at all, but it's not a bad idea to have one.
Good luck to you.
Michael S. Haber is a New York attorney. As such, his responses to posted inquiries, such as the one above, are limited to his understanding of law in the jurisdiction in which he practices and not to any other jurisdiction. In addition, no response to any posted inquiry should be deemed to constitute legal advice, nor to constitute the existence of an attorney/client or other contractual or fiduciary relationship, inasmuch as rendering legal advice involves the ability of the attorney to ask appropriate questions of the person seeking such advice and to thus gather appropriate information. In addition, an attorney/client relationship is formed only by specific agreement. The purpose of this answer is to provide the questioner with general information, not to outline specific legal rights and remedies.
A good place to start is to figure out what are you gaining and what are you giving up by entering into an agreement. If there is no gain for you, do not sing anything giving up your right. Signing a covenant not to compete can land you in court at a later time. My experience is that if the employer is willing to offer you something, you will receive a proposed agreement for review. Good Luck.