A non-compete agreement, or covenant not to compete, can’t prevent you from leaving your current job or accepting a position elsewhere. Your employer can’t force you to stay; the 13th amendment to the Constitution prohibits “involuntary servitude,” and the U.S. fought a civil war over this very matter. Also, your current employer can’t stop you from using your job skills to work and earn a livelihood.
Courts and judges are predisposed to disliking non-compete agreement; the presumption is that they’re invalid bullying tactics imposed by employers. Fair competition’s considered to be a good thing in this economy, and the legal system wants people to be gainfully-employed, responsible members of society. Impediments to healthy competition or earning an income are generally looked upon unfavorably. In some states, non-compete agreements are automatically void as a matter of law. In other states, they apply only to owners and key executives, not to rank-and-file employees. In still other states, they’re valid only to protect legitimate business interests, such as preventing someone from stealing a trade secret or leaving with client files.
You might want to do some online research about your own state’s law. Regardless of where you live, however, your current employer can’t violate public policy or oppressively restrict your ability to earn a living.