After hours of ES2 play, I noticed sometimes you get population from other major/minor faction that are right next to your system.

There are usually an icon on the star system management panel to indicate if any pop is migrating from or to your system.

To be clear, by passive migration I meant the population you get on a colonized star system for free from other factions (as you wait and play normally). Not migrating between planets in a star system, not migrating between lv2+ star systems, and not migrating to outpost.

I can't find any detail on how this mechanic works. Does it have to do with approval rate (maybe relative to adjacent enemy star system)? Does it have the restriction of only happening between adjacent star systems (seem to be the case for me)? Would political tendency be a factor here? Would empire relationship be a factor here (like at least friendly with minor faction)?

Any information on this would be appreciated.

From what I have observed it is usually from a minor faction to your next free system. My best guess is good faction relationship should be enough.

My working theory is if the food on system becomes insufficient, population, rather than dying out, just gets up and leaves to the next available system. You can also observe this when you invade a system and retain a low ownership, as long as you can't feed them, they get up and leave. Whether it applies to minor factions is uncertain, but they do migrate, perhaps there is a population cap.