Shadow (under his real name Clyde) and Baram were train robbers. After a particularly successful robbery in which they made off with a million gil, Baram suggested they call themselves "the Shadow Bandits" since their feat was worthy of naming the duo.
The two went on the run from the authorities and Baram was injured. He urged Clyde to get to safety but first asked Clyde to kill him, afraid of what would happen to him if he got caught. Clyde refused and fled, leaving Baram to his fate. Clyde escaped to Thamasa where he got married, and fathered a child before he left town to keep his past from catching up with him, taking the alias "Shadow" from his time with Baram.
After Kefka Palazzo is defeated, Shadow stays behind in the collapsing Kefka's Tower while everyone, including his dog Interceptor, return to the Falcon, saying "Baram... It looks like I can finally stop running... Come and find me all right?"
Behind the scenes
In the scene where Baram asks Clyde to kill him, he uses the same sprite as the Returners. In-story it is possible Baram had joined the Returners, or had donned their outfit as a disguise, but it is not known if the Returners existed ten years ago. Another explanation is that this was done due to technical restraints—Baram's normal sprite, used throughout the game for bandits, does not have a "fallen down" pose. It is possible the developers gave Baram the Returners' sprite to make use of this animation the bandit sprite lacked, and then for whatever reason retained the bandit sprite in Baram's other appearances.
Baram is Korean for "wind". The name "Baram" bears a vague resemblance to "Bonnie". Together with Clyde, the two could be a reference to the famous thief duo, Bonnie and Clyde. Alternatively, it may refer to the real Clyde's last name, Barrow.
Baram's Japanese name, Billy, is likely a reference to Billy the Kid.