I could be slightly clearer on the question but I'll say a little about how this relates to my own experience. I'm not an immigrant but I do live and work in Thailand, for 9 years now. Things change related to obtaining immigrant / permanent residence status, which I'll say a little about.
There is no background check here related to getting different kinds of visas or work permits. Someone could live out their life here as a non-resident worker without ever facing any review. Per my understanding to become a permanent resident, a different process, a criminal background check is required, although I wouldn't know what they are screening against, what findings or background is grounds for rejection. I'm not sure which category retirement visas fall into, if there is a similar screening for that or not.