As a PE, they can face significant legal repercussions for errors in work they approve.
The benefit to the PE is that many Civil Engineering projects are legally required to have a PE design/approve them. The PE literally has a physical stamp they use to stamp blueprints and designs when they approve it. Work won't proceed without that stamp.
So, if a PE refused to approve a bridge design, presumably it would be very difficult to find another PE who would approve it (especially given the record of the first PE rejecting the plans) and the work would not proceed.