That would be constructive dismissal, and (certainly in many parts of the world) you could take them to an employment tribunal over it.
I worked at a company once that was bought and tried the same thing. I told them I needed a large compensation component to sign, and I never heard anything else about it. This was big company buying big company though, so it was probably boiler plate stuff.
When my last company got bought, they tried to throw that in for existing employees, but it was a 3 year time period. I refused. They said my job depended on signing. I know I could pursue a number of legal arguments as to why that wasn't valid, but I went with my own standard advice to not work with bullies, and I quit.