  Strain tuning is a powerful experimental method in probing correlated
electron systems. Here we study the strain response of the lattice dynamics and
electronic structure in semiconductor Ta$_2$NiS$_5$ by polarization-resolved
Raman spectroscopy. We observe an increase of the size of the direct
semiconducting band gap. Although the majority of the optical phonons show only
marginal dependence to applied strain, the frequency of the two B$_{2g}$ phonon
modes, which have quadrupolar symmetry and already anomalously soften on
cooling under zero strain, increases significantly with tensile strain along
the $a$ axis. The corresponding Gr\"uneisen parameters are unusually large in
magnitude and negative in sign. These effects are well captured by
first-principles density functional theory calculations and indicate close
proximity of Ta$_2$NiS$_5$ to a structural instability, similar to that
encountered in excitonic insulator candidate Ta$_2$NiSe$_5$.
