A hole in a 4d orbital of atomic xenon relaxes through Auger decay after a lifetime of 3 fs. Adding electronegative fluorine ligands to form xenon fluoride molecules, results in withdrawal of valenceelectron density from Xe. Thus, within the one-center picture of Auger decay, a lowered Xe 4d Auger width would be expected, in contradiction, however, with experiment. Employing extensive ab initio calculations within the framework of many-body Green's functions, we determine all available decay channels in XeFn and characterize these channels by means of a two-hole population analysis. We derive a relation between two-hole population numbers and partial Auger widths. On this basis, interatomic electronic decay processes are demonstrated to be so strong in the xenon fluorides that they overcompensate the reduction in intra-atomic Auger width and lead to the experimentally observed trend. The nature of the relevant processes is discussed. These processes presumably underlie Auger decay in a variety of systems.