From wikipedia - https://en.wikipedia.org/wiki/Bounty_jumper

men who enlisted in the Union or Confederate army during the American Civil War only to collect a bounty and then leave.

A month after the Battle of Fort Sumter the United States Congress passed a law allowing for bounties up to $300. The Confederate government did likewise, starting at $50 and then later in the war increased the bounty to $100.

As the typical Northern private was paid $13 a month, the bonuses were considerable.

Risky, since desertion for them could mean torture or execution, but the money was really good for the time.

I was curious about the “bounty” aspect.

The Enrollment Act of 1863 instituted conscription but allowed individuals to pay a bounty to someone else to fight in their place. Bounty jumpers commonly enlisted numerous times in the army, collecting many bounties in the process.

The article about the Enrollment Act of 1863 also provides a good explanation

Substitutions were available throughout the war. The problem with substitution was that it provided substitutes with powerful incentives to desert soon after enlisting. Career "jumpers" made a living by enlisting as substitutes, collecting their compensation, deserting before their units were dispatched to the front, and repeating the process.

Rich man's war, poor man's fight as it was called.

Valid for many wars before and still valid today

As a side note, I'm aware that Brazil did something similar back in the Paraguay War, but the person who wanted to avoid being conscripted had to pay the govt and offer another person in their place - who would either be bribed or threatened into accepting going as the substitute.