There is much information available about licencing for hams who take
temporary trips aboard. But what about people who are Permanent
Residents and want to become a ham? Do most countries allow Permanent
Residents to obtain an operator's licence? a station licence? all
without needing to return or have any paperwork from one's country of origin?

I'm not talking about Reciprocal Licensing, I believe. I'm taking
about citizens of country A who have long ago moved to country B where
they are now Permanent Residents, when one day the ham bug bites and
they want to get into ham radio for the first time. They may live
very far from country A and don't want to go there anymore.

How far does the average country B allow them to get as far as
licencing as compared to citizens of country B?