I wouldn't give up any salary if the job is in the city where I live. I would rather be in the office to connect with people and to have structure.
If I had to live elsewhere, it would depend on the cost of living. In SE Asia for example, I would give up 60% or more. In Europe, I would give up only 20-40%.
It's not about where you have to live, but where you want to live. The whole point of remote job would be the ability to move to whatever place you like.
I would love to live in the Philippines and pull an American salary. The cost of living is easily 50-70% cheaper than Los Angeles, and the people there are so friendly.
If your company uses (or could use) offshore workers, you could have a good case for moving overseas to manage that team. The value of having someone they trust working alongside the offshore team is probably worth paying you your current salary.
If I had to live elsewhere, it would depend on the cost of living. In SE Asia for example, I would give up 60% or more. In Europe, I would give up only 20-40%.