I've never seen a comprehensive list, personally. That said, in most of the cases that I've seen in my research into New York and Pennsylvania units, the missing were usually killed in action and buried in either mass or unmarked graves on the battlefield. Especially after the war, it was usually determined if someone was a prisoner and their names were moved from the "missing" list to the "captured" list but, as with all things, there were exceptions with men slipping through the cracks.
For the relatives of the missing, they can only console themselves with hope that after the war, perhaps their remains were found and removed to national or state cemeteries.
Ryan