Once the hammer has fallen, the sale is agreed and contracts are exchanged. At this stage, neither the seller nor the buyer can pull out.
On the very rare occasion that the buyer fails to complete in accordance with the contract, then a contingency process is followed and the buyer risks losing their deposit and incurring further penalties.
A buyer also cannot try to renogotiate their buying price after the auction, this is called gazundering. The fact buyers can't do this is a key benefit of selling property at auction compared to selling at an estate agents.