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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 $3+1+\mathrm{Decay}$ , 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 $g^2=0$ , ${\sin }^2\left(2{\theta }_{24}\right)=0.16$ , and $\mathrm{\Delta }{m}_{41}^2=3.5{\mathrm{eV}}^2$ , in agreement with the recent $3+1$ sterile neutrino search. Values of $g^2\ge \pi$ are excluded at 95% confidence level. This result substantially limits decay parameter space indicated by recent global fits, disfavoring the decay scenario.