Some might ask you to sign what I call a "back-door" training contract, AKA, a non-compete....often because some states, like NH, have laws that nullify training contracts, or make them hard or difficult to enforce.
Basically states if you leave, you cannot fly the same aircraft type without repaying the training cost and or work for another company flying the same equipment in a set geographic region.
Phraseology can vary, but the intent is to make hard to take a job, get trained, then use the training and experience you just received to get a better paying job in the same area.
Do ask before you accept a job.