Depends on the object. In conductive solids, a portion of the electrons sre shared out thoroughout the solid, so there's no single atom laying claim to them. Any lost electrons will be from that sea of valence electrons.
In a nonconductive solid (and you'd be amazed how hard it is to find one of those, most are simply badly conductive), the electrons will come from a location and keep on missing there, if you can prevent them being replaced from the environment. That location will rarely ba an atom, though, but more usually a molecule, which again will have a few electrons shared throughout the molecule (binding electrons), so losing one electron will change the charge distribution of the molecule, but will be very hard to pin to one specific atom.
Neutralizing that positive charge - if there are less strongly bound electrons in the vincinity, that will happen much faster than within seconds. In a good vacuum, it won't ever happen.