The Nomad Capitalist attempted to address this issue in an article and video.
The Cheapest and Safest Countries to Live In
A lot of their suggestions are in Eastern Europe. I have zero experience in that area (hopefully rectified soon), so I can’t weigh in there.
With regards to places I’ve visited, I think I could live safely for less than $2000 a month in the following countries:
I’d also consider Costa Rica, Chile, Singapore, and Belize as safe locations, but they may require a little more money to live a lifestyle similar to what you may be used to.
Check out the article for another take on the issue.