No worries. I’ve briefly touched on it but not in its
entirety.

I’ve boiled it down to three main categories:

Involuntary circumstances: 

This occurs when a nation is conquered and is forced to live
with their conqueror/ annexer.

Ex: Chibitalia
and Austria under the HRE household.

Source:
Hetarchive, Chibitalia (Main storyline.)

Wartime Circumstances

When administrations crumble and there’s no other place to
go…

Ex: England hosts
France during the Vichy Regime.

Source: Volume 5, 

Liberté, Égalité, Fraternité and…

Employment
Circumstances

Due to their dire financial circumstances, Lithuania and
Romano move into America’s house and end up working for him.

You could argue that this is in a way, involuntary, but I
would say it’s more along the lines of necessitated.

Source: Hetarchive/ Hetascanlations, World Stars Chapter 58 + Lithuania’s Outsourcing Series