Electron detachment thresholds of metal cluster anions, MN-, are a few electron volts. The excess electron is therefore detached by visible or ultraviolet light, which also creates low-lying bound electronic states, MN-*; i.e., MN-* energetically overlaps with the continuum, MN + e-. Here, we perform action spectroscopy of photodestruction, leading either to photodetachment or to photofragmentation, for size-selected silver cluster anions, AgN- (N = 3-19), to unveil such bound electronic states embedded in the continuum. The experiment takes advantage of a linear ion trap that enables us to measure photodestruction spectra with high quality at well-defined temperatures, where bound excited states, AgN-*, are clearly identified above their vertical detachment energies. Structural optimization of AgN- (N = 3-19) is conducted by using density functional theory (DFT), which is followed by calculations of vertical excitation energies by time-dependent DFT to assign the observed bound states. Spectral evolution observed as a function of cluster size is also discussed, where the optimized geometries are found to be closely related to the observed spectral profiles. A plasmonic band consisting of nearly degenerate individual excitations is observed for N = 19.