A Reverse greenshoe is a special provision in an IPO prospectus, which allows underwriters to sell shares back to the issuer. If a 'regular' greenshoe is, in fact, a call option written by the issuer for the underwriters, a reverse greenshoe is a put option.
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Reverse greenshoe has exactly the same effect on the share price as a traditional option but is structured differently. It is used to support the share price in the event that the share price falls in the post-IPO aftermarket. In this case, the underwriter buys shares in the open market and then sells them back to the issuer, stabilizing the share price.
In certain circumstances, a reverse greenshoe can be a more practical form of price stabilisation than the traditional method.
How regular greenshoe option works
How reverse greenshoe option works
References
Reverse greenshoe Wikipedia(Text) CC BY-SA