My wife moved from Japan to the US some 10 years ago now. She came over initially on a student visa, which allowed her to work for a limited number of hours per week and only where she attended school. For example, she worked at the school's book store, then helped out with cleaning classrooms and shit.
After a student visa, she got a working visa, but that has a shorter duration. I believe it's like 1 year maximum, or something similar. They didn't offer back to back working visa's either, so she had to apply for a second student visa after the working visa expired. What sucks about this, is she was becoming a nurse, making a decent amount of money and paying taxes, but the government refuses to let you work and pay taxes without a working visa, and they're limited. She fought that battle for a while until I came into the picture and eventually got married. It was a real pain in the ass until that point, though. The US makes shit really difficult if you want to be completely legal here. It's easy if you're illegal, though. Stupid how that works.
I couldn't comment on moving from the US elsewhere, but I'm sure it would be similar. Maybe not as severe as that, but you never know.