Unless you're planning on going out and shooting someone with it, what does it matter? Are you planning on having the police check into the firearms you own? I'd buy it, buy a new stock so it doesn't have someone elses name on it, and call it a day.
It's probably not stolen, and if it is then the person who it was stolen from hasn't reported it/didn't know its serial number because the pawn shop would have found out when they recieved it. So, yeah- it COULD be stolen- but if it is, no one knows and no one cares. (just like anything else you buy from a pawn shop)
Its not as if the cops are going to run a ballistics test on the BB's lying out in the skeet range that you fired and find some way to link you to a murder. Guns are legal, owning a gun you purchased(be it from a Gun Store, Private Seller, or Pawn Shop) without any knowledge of it being stolen is legal.
Perpetuating the image of gun ownership as being full of red tape or that there are all sorts of 'legal' problems with gun ownership is a huge problem right now.
Its the reason why everyone assumes that silencers, special ammunition types, fully automatic weapons, high-cap magazines, open carry etc are illegal.
You want a gun? Buy it. Want a silencer? Pay the fee to your local sheriffs office and buy it. As long as YOU aren't doing anything illegal, let the dealers assume the risk of stolen firearms.