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This Letter extends a recent IceCube sterile neutrino search to include unstable sterile neutrinos within the context of a model termed 3+1+Decay, which expands upon the 3+1 model by introducing sterile neutrino decay to invisible particles with coupling constant g^{2}. The model is attractive since it reduces tension between oscillation experiments within the global fits and with constraints that come from cosmological observables. The analysis uses 10.7 years of up-going muon neutrino data with energy 500 GeV to 100 TeV and with improved reconstruction and modeling of systematics. The best-fit point is found to be g^{2}=0, sin^{2}(2θ_{24})=0.16, and Δm_{41}^{2}=3.5 eV^{2}, in agreement with the recent 3+1 sterile neutrino search. Values of g^{2}≥π are excluded at 95% confidence level. This result substantially limits decay parameter space indicated by recent global fits, disfavoring the decay scenario.