When and how can a soldier void their contract?

You cannot void your contract unless your contract was defective, unfulfilled, fraudulent or erroneous, and the contract cannot be renegotiated.
Like any business contract, it is legally binding and one party can't choose to void a contract without the other party's consent. That's the whole point of a contract.

If the service member has not gone to basic then there is a chance, other than that it is virtually impossible.

So this Soldier was promised something, right? Is it in their contract? Do they meet all stipulations of said incentive? If so and their unit is not helping then reach out to IG. However, if it's not in their contract, it's their fault for not reading it. Remember, we are all adults, not kids when we sign these contracts. If this Soldier was a 17 year old at the time of signing their contract then mommy and daddy should've evaluated the contract before letting junior go be a Soldier.

That said, I hate these obscure questions. Always lay out details so we are not guessing.