Expanding on my previous comment with an example: I obtained a long term residency visa a few months ago. I was in the country at the time and didn’t want to fly 15 hours back to my home country, and the embassy in the neighbouring country only accepts applications from residents, so I flew to another nearby country which does accept non-residents. The country that I have a visa for doesn’t care where the visa is issued, it’s the individual embassies that set their own rules about who they will process applications for. You just have to look through each embassy to find one that accepts you (which will be documented on their website). Except now for the U.S. which is instituting this rule.