The problem of a quantum Ising degree of freedom coupled to a gapless bosonic mode appears naturally in many one dimensional systems, yet surprisingly little is known how such a coupling affects the Ising quantum critical point. We investigate the fate of the critical point in a regime, where the weak coupling RG indicates a flow toward strong coupling. Using renormalization group analysis and numerical density matrix renormalization group (DMRG) calculations we show that quantum fluctuations near the critical point cause phase separation on an emergent long scale, and the transition becomes first order. This suggests the existence of a tricritical point with potentially exotic properties.