Move Abroad by Working Remotely

The view from our bedroom in
our home in La Rochelle, France

Did you know that many countries allow you to live there even if you can't work there? I've hinted at this when I wrote about moving to Uruguay, but this is a more widespread thing than you would realize.
It works like this (with lots of hand-waving because different countries have wildly different laws): you have residence permits, and work permits. You usually get the former with the latter, but not necessarily the other way around. If you have a work history of working remotely and can show a decent income, many countries will allow you to apply for a residence permit.
Despite having written on the topic of "how to become an expat" for years, I've not paid much attention to the remote working aspect of it. I've touched on the logistical problems of working remotely, but I'm kicking myself for not realizing that the practice of issuing residence permits for remote workers is more widespread than I realized. This blog post details one family's research into living in Europe with remote work, but it's short on practical details. I suspect part of the problem is one I've struggled with repeatedly: laws in this area are not well-publicized and change frequently.
After asking, I was pointed to this Spanish Consulate visa page which describes "Residence visa with Non-Lucrative purposes" (whatever the hell that means). It's apparently the visa process that allows you to live in Spain so long as you have sufficient income. It's complicated, takes about three months and, in the lovely words of the page: ADDITIONAL REQUIREMENTS MAY APPLY (their words and emphasis). One of the requirements is:

Proof/s that you have sufficient financial means for you (and your accompanying family) during the stay in Spain without the need to work translated into Spanish.

Ignoring the awful, awful grammar: what does "sufficient financial means" mean? Who the hell knows? According to the blog entry that tipped me off, Italy requires a €50K annual income and Spain is apparently less, but that's all I know.
Meanwhile, Forbes has an article about the best-paying remote jobs. I currently take contracts remotely, but I have a specialized background (mostly IT related). Medical transcriptionists need a bit of training, but not overly difficult. You won't get rich doing that, but with a salary between $30K (US) and $50K (€22K to €37K), you can earn enough to survive in most of Europe, so long as you steer clear of the biggest cities. Personally, I find the smaller towns more pleasant, anyway.
Anything IT related, writing and editing jobs, and even public relations people can work remotely. In fact, there are plenty of remote jobs available, with varying salary levels, If you target South America, Africa, Eastern Europe or many parts of Asia, you should easily be able to afford to live abroad. The hard part is navigating through the laws that get you a residence permit based on your remote income (in my experience, South America is the easiest for this, but I hear good things about parts of Asia).
Good luck and start looking for a new job! If you know anything about these types of residence permits, let me know.