Fab fragments of antibodies to fight viral infections
There are three pathways by which soluble antibodies (which is what the Fab fragments arise from) can inactivate viruses (from Janeway's Immunobiology):



What you describe with the Fab binding to the viral receptors is a type of neutralization. Janeway claims that the type of naturally occurring antibody primarily responsibly for neutralization, IgA, is mostly exported to mucous secretions, so presumably it gets digested/excreted along with the rest of the mucous proteins.