We present a search for an unstable sterile neutrino by looking for a resonant signal in eight years of atmospheric νμ data collected from 2011 to 2019 at the IceCube Neutrino Observatory. Both the (stable) three-neutrino and the 3+1 sterile neutrino models are disfavored relative to the unstable sterile neutrino model, though with p values of 2.8% and 0.81%, respectively, we do not observe evidence for 3+1 neutrinos with neutrino decay. The best-fit parameters for the sterile neutrino with decay model from this study are Δm412=6.7-2.5+3.9  eV2, sin22θ24=0.33-0.17+0.20, and g2=2.5π±1.5π, where g is the decay-mediating coupling. The preferred regions of the 3+1+decay model from short-baseline oscillation searches are excluded at 90% C.L.