Are there furniture items that can't be changed or removed from a villager's home?

[Lavandula]

No buying but the villager can give you back the bug or fish. I got the scorpion back when I gave Sterling an item inside his house.
Noticed that my 2nd town likes to give bugs/fish back a lot.

I agee. I've had them give me their bugs or fish when those items were replaced with something else, whether it be another bug/fish or actual furniture item.