So, yes, they will go away when your money runs out.
I think Mythologique was talking about what if you wanted to yank it before the time/money ran out.
It reminds me of https://www.sindome.org/bgbb/game-discussion/ideas/fire-damage-and-graffiti-882/
RP is what GM's are here for. Players should appreciate the idea that puppets can and do do things for your character which code doesn't support. There hasn't been one GM so far who has weighed in and said "yes please" to this feature. If it happens, that will change things.
Cerberus, please @bug this as an @idea if it's something you're interested in.