Jackson was a member of the DHARMA Initiative. He was holding a gun, and was touched by Lowell before the 1977 Barracks battle happened. It is possible that Jackson survived the battle, as he was not seen being killed.
Jackson's jumpsuit had no logo, and the incription of his job was not clear.
He may have been killed along with other members of the DHARMA Initiative in the Purge, or he may have left the island sometime between 1977 and The Purge.