I'm lucky - my employer was sympathetic to my situation, I had built good relationships with senior management, and what I do (I'm not an engineer) is a skill that they don't have in abundance, and I had a global role in any case.
All these factors contributed to them moving me to Canada without a major hit to my salary.
There is a difference (I get paid about USD 10K less), but that's more than made up in the lack of healthcare costs (I pay absolutely nothing for healthcare coverage in Canada), and most importantly for me, peace of mind.
Also, I couldn't realistically switch jobs in the US without tons of paperwork. As a PR, I am treated exactly like a citizen and could easily switch if I got a better offer.