I recently took a job with a paycut of about 8%, and I have absolutely no regrets. My life/work balance is great now, I get lots of time for vacation because of the way my schedule is set up, and I now only work a few minutes from home instead of a longer commute. The crew I work with is great, the boss is so much better, and the job itself is much better. It's like a light switch was flipped. The paycut worried me more at first, but now, I know it was the best move and completely worth it.
In your situation, are you considering everything? It's not likely just a pay difference, but possibly housing too (depending on if you get a housing allowance or not). And maybe more, I don't know.
A 50% cut is pretty steep, and I was not in the position to take that big of a hit. However, if I wasn't helping my son with college (he's living at home and going to a community college the first two years), I could have sold my house, bought a much smaller house, would not be saving to help with the college, could have sold my land, etc, if I thought it was worth it. And I could have been happy. I might have to push back retirement, but maybe not. Maybe downsizing so much early would work out well. I have a good base in my retirement account (compound interest!), so I could have relaxed on contributions, although I would not have stopped them.
I've seen people leave my current position in the chase for money. Two are actively trying to come back (they went to new locations). The ones who have been promoted to the next level up from mine often say they only did it for the money, and they really pretty much hate the job/responsibility now, and wish they could drop back down (but are "addicted" to the money). I have no plans to chase the money, even though I know I could make about 20% more if I went for the promotion. Nope, perfectly happy to stay where I am.