If someone is an existing employee and you want them to sign a new employee agreement, you need some additional consideration besides "we let you keep your job," such as an increase in pay.
IANAL but 'icebraining is accurately describing US law. We nerds in the US need to fully internalize what the law is before we can fight it.
Contracts require consideration[1]. If we agree you will give me $400 tomorrow, that is not a contact. If we agree that I will give you $200 today and you will give me $400 tomorrow, that is a contract.[2]
[1] http://en.wikipedia.org/wiki/Consideration
[2] There are other components that make contracts legal; technically I'm only describing the consideration aspect.
One of the most common principles across a wide range of jurisdictions is for the default assumption to be that the salary compensates for the tasks and duties carried out in the contract period only.
Further, there's a public policy concern, in that non-competes in extreme cases can make a person unemployable during the period, and force this person onto welfare programs, and society as a whole thus have an interest in ensuring that consideration for potentially making you unemployable is made explicit and coming due if/when you're actually prevented from taking up a job.
This is very important, and something that very often gets lost in discussions of employment contracts, minimum wage etc etc.
The prospective employee needs to make rent. The prospective employee needs to eat. These are very basic and powerful motivations and we (as a society) should not let business take advantage of these to low-ball on pay or impose onerous contract terms.