It is used by low-level players in Multiplayer and a very popular and good starter weapon for low levels.
It has increased damage in Multiplayer: about 25-30 HP damage provided one has Common Clothing on.
This weapon can be won in the Bronze Bullet Chest lottery that can be played for free during the lottery tutorial.
It is also the weapon used by Confederate Soldiers. However, in the mission "Plague Outbreak," the soldiers use Rusty Guns instead of Burneside Carbine. If you kill one of the soldier, it cannot be obtained.