Rav Eliezer Papo (1786-1827), in his Hesed La’alafim (listen to audio recording for precise citation), addresses the case of two people who made bids for an honor in the synagogue, such as an Aliya, and the Gabbaim know that the higher bidder will not be able to pay the pledged sum. He writes that in such a case, the Gabbaim must grant the Aliya to the lower bidder, rather than call up the higher bidder and lose the pledge. The lower bidder may not refuse the Aliya by saying that once a higher bid was made he is now absolved of any commitment.
Importantly, the Hesed La’alafim adds that this applies only if the Gabbaim can find a discreet and appropriate way to grant the Aliya to the lower bidder, without embarrassing the higher bidder and without causing discord and controversy. He emphasizes that it is preferable to forfeit millions of gold coins to avoid humiliating another person or causing a fight among synagogue members.