I was thinking about Half-Life 2. There are some very H.R. Giger connections there. Indeed, if you look at the original textures for the headcrabbed zombies the "face" of the scientist comes through on the "top" of the headcrab as an eye socket/skull look, very similar to Big Chap.
Anyway. Dr. Kleiner keeps one of the headcrabs as a pet. He says she's been "Debeaked." Which I take to mean "she" can no longer attack a victim and take over their nervous system.
I thought... I wonder if the same could be done to a facehugger. Supposing you could capture one, restrain it, and eliminate its means of impregnating, could they become a domesticated "pet" animal? Would they have a particularly long life cycle once removed from the egg if not forced to deliver their goods right away? Even with its primary motive in life removed, would it still seek to serve the alien species in some other manner?