Employee Rights?

In the US, no they cannot force you to stay, though they can of course have a contract with consequences for breach, i.e. you owe the training costs back, etc.

You can't force anybody to do anything but you can enter into a contractual agreement. For example, you could have the employee pay for their training with a loan but after they have been on the job for a year or if the company determines they are a bad match for the job for any reason, the loan will be 100% forgiven. If the employee quits before one year on the job the loan will become due within seven days. A lot of people, including me, however, would never take that job.

No one can force you to keep a job you don't want to keep.   However, there are consequences for violating and employment contract.   You'll have to read the contract to see what they are.

As far as the military goes, they are not your regular type of employer.   Go AWOL and they can toss your butt in jail. 

There is no supporting evidence. No Company can force someone to stay in a job. 

That Contract would be unenforceable.

Not without a written contract.. Even then it will depend on the state where they work and if non complete agreement are enforced.

The military is not a normal employer. Other companies can have clauses like that, but they are not enforceable.