Baxter only appears in Mark's dreams, which serve as flashbacks to his past, much like Thomas' dreams. He appears in Mark's dream when they had a near-death experience due to the subtrans station flooding after the Sun Flares melted the polar ice caps. Alec saves Baxter after almost suffocating in the boiling hot water.
Later, in another one of Mark's dreams, a man only known as the Boss and his female partner reach the Lincoln Building on a large yacht and order Mark's group to raise their hands. Alec raises his hands too slowly, prompting Boss to shoot Baxter. He dies before he hits the ground. Mark has this dream the most often.