Backstop Purchaser
  
This is not a baseball team that signs up all the catchers they can find. Rather, a back-stop purchaser buys the leftover shares from the underwriter of an equity or rights offering. In that way, a back-stop purchaser is like an insurance policy. The purchaser guarantees that a company (and/or its investment bank) will raise the cash it needs to raise.
Example: Company A is going public. It plans to issue 10 million shares in an initial public offering (IPO). Bank B agrees to underwrite the IPO. Bank B does its research, or due diligence. Feeling good about the deal, Bank B agrees to sell the 10 million shares for $25 per share.
Bank B also comes to a special agreement with a wealthy hedge fund guy, Mr Hedge. Mr Hedge agrees to be Bank B's back-stop purchaser. If Bank ABC can't sell all the shares in the IPO, Mr. Hedge agrees to buy those leftovers. Being no dummy, Mr. Hedge obtains a fee for agreeing to be the back stop. He is taking on the risk of having to purchase and then trying to reissue Company A's securities.