Update!
The stock was hard to remove, but appears to be there from the beginning, meaning not attached afterwards. It was screwed on the metal part that was hanging. You can see the side tabs (held by two screws) that have broken, and the gravity was pulling the whole assembly down.
Pics are not top quality, but the dslr helps a lot.
EDIT :
I opened the gearbox, seems like the piston is stripped, looks like making this gun functional will be somewhat easy, if I can close the gearbox without breaking it. God this thing is complicated!