Only the clearing members (big broker/dealer) of NYSE can trade on it. When you or any investor sells IBM short  using GS as a broker, NYSE always sees the trade under GS’s name. If investor can’t fulfill the obligation, GS is responsible.
Technically, GS “sponsors” your trade. I think most trades are sponsored this way (except trades GS does using its own money). A sponsor member like GS has to protect itself.
A pass-through broker who simply passes the order to the exchange without any check is running the greatest risk.
Same thing in other exchanges. I traded commodities in 1997. My broker was responsible to answer clearinghouse’s margin calls if I don’t. Integrity requires all margin calls satisfied (or clearinghouse has the right to liquidate your position). I had an account with the broker, not the clearinghouse, so all the positions were held under first-tier broker’s name, i.e. a member of the exchange.
 regular sell or buy also involve responsibilities and obvious financial risks to the broker.