Assume the company is in Delaware and been taken over by a larger corporation: If one already has the job, is it possible to for the larger corporation to compel existing employees to sign non-compete agreements?
Assume subject is in DE and is a W2 employee (no contract or 'term')
A company generally cannot compel an employee to agree to a non-compete, but they have a wide variety of alternatives for inducing employees to do so. Most obviously, they may threaten to fire employees who refuse, whether immediately or at the end of their current term, as another answer observes. Indeed, if Big Company makes an NC a condition of employment then they are likely to insist on the same for employees they obtain from Original Employer.
Firing employees for refusing to sign does, of course, put them in the job market as potential competitors, but the company may well find it acceptable to do that on their own terms. In particular, Big Company can ensure that those who won't sign go out the door with minimal knowledge of Big Company's clients, trade secrets, etc. other than those obtained from Original Employer.
And that leads into other forms of inducement. Big Company can do some or all of the following things, depending on the particular employment situation:
Some of those fit directly into Big Company's perceived interest in avoiding employees using Big Company internal information to jump ship and compete with them, and others could fit into Big Company policy about which jobs require an NC. Some are just pressure tactics, but that does not necessarily make them unlawful (nor are all variations on the others necessarily lawful).
I assume you are working in the US outside Montana (corporate headquarters is not so important). It depends on how long they are presently required to keep you on. If you have an at-will contract (most likely), they can present you with a "sign or be terminated" ultimatum. In case you have a term employment contract, you can be forced to sign at the end of the term.
Can they? Well, they'd sure like it if you signed. I'll guarantee you that their agreement is entirely to their benefit, and not to yours. This happened to me once, back in the halcyon days of the 1990's. The company I worked for (a small-to-middling size contracting firm in the wilds of northern Ohio) was being sold to a large-ish national contracting firm who wanted us all to sign their non-compete. I liked the agreement I had with the local firm and wanted to keep it, but knew that if I said anything like that I'd be told "Nope, you gotta sign the new company's agreement". So I did what anyone does in a situation like this - I punted. "Gee", said I, "I'll be happy to sign this...just as soon as I have my attorney take a look at it". I wasn't refusing - I was just saying I wanted my legal adviser to look at a legal document prior to signing it, which is entirely within my rights to do. The harried administrative guy didn't even bat an eye - he just said, "Fine, sure, sign it and get it back to the office as soon as you can, OK?". I assured him I would, we shook hands, and neither of us ever saw the other again. I did actually take the agreement to my attorney, whose comment on it was, "Well, it's interesting to see they've re-legalized slavery...". I asked him whether or not I should sign it, and he asked, "Will they fire you if you don't sign?". I told him I didn't figure they were likely to do so, as it'd mean they'd get no revenue from having me work for them, so he said, "Don't sign it, don't say anything, and see what happens". I never signed it. Nobody ever asked me about it in the eight to ten years I remained with that company. Nobody knew, and nobody cared.
IANAL, and this is not legal advice. But you might consider telling them that your attorney has to look it over, and then...do whatever your attorney tells you to do, based on the document in front of you and your situation.
:-)
