Using neon and its dimer as a specific example, it is shown that excited Auger decay channels that are electronically stable in the isolated monomer can relax in a cluster by electron emission. The decay mechanism, leading to the formation of a tricationic cluster, is based on an efficient energy-transfer process from the excited, dicationic monomer to a neighbor. The decay is ultrafast and expected to be relevant to numerous physical phenomena involving core holes in clusters and other forms of spatially extended atomic and molecular matter.