can my boss force me to sign with the new company that bought his business and deny me severence?

No one can force you to sign anything. But without a contract or policy severance is not required of any employer. So if your employer pays you lawful consideration, which can be almost anything, you may be giving up rights to challenge agreements which otherwise might not be enforceable. No lawyer can advise you on noncompetition provisions without knowing much more about what you do, who you do it for, and by reviewing the terms of the agreement you might sign. One thing that is almost certain is that in most cases employees have 7 days to rescind or revoke a signed agreement. In most cases employees have 21 days to review severance provisions, at least in New York, plus another 7 days to decide not to accept the terms. Your best option would be to pay an employment lawyer to review the agreement before you sign it. Today, many of us do so for flat rates and we do that for clients statewide. Seeing a lawyer in person is becoming more rare for many of us. Good luck. Retain an employment lawyer is your best option before signing.