Dear Siva, The question of issuing or not issuing an appointment letter is secondary for the following reasons:
1. A contract or agreement could be oral also. If it is in writing and consent of the parties is available on records, it is fine. Legally, an oral agreement is also valid.
2. The person in question was in the office, would have signed the attendance register and other documents. They would have entered his name in the entry and exit register and other documents. "By estoppel," he has been an "employee," whether you pay/paid him or not.
So now the question is what to do with him in this scenario? Precisely, it is not worth pursuing him anymore. In case he asks for his pay or any other documents like an appointment or experience letter, then you can handle it differently when the need arises. For the present, to legally or logically close his case, prepare his pay for the days "he worked" and keep in "arrears * unclaimed suspense." There ends the matter.
kumar.s.