Abstract: Using spin- and angle-resolved photoemission spectroscopy and relativistic many-body calculations, we investigate the evolution of the electronic structure of (Bi1-xInx)(2)Se-3)(2)Se-3 bulk single crystals around the critical point of the trivial to topological insulator quantum-phase transition. By increasing x, we observe how a surface gap opens at the Dirac point of the initially gapless topological surface state of Bi2Se3, leading to the existence of massive fermions. The surface gap monotonically increases for a wide range of x values across the topological and trivial sides of the quantum-phase transition. By means of photon-energy-dependent measurements, we demonstrate that the gapped surface state survives the inversion of the bulk bands which occurs at a critical point near x = 0.055. The surface state exhibits a nonzero in-plane spin polarization which decays exponentially with increasing x, and which persists in both the topological and trivial insulator phases. Our calculations reveal qualitative agreement with the experimental results all across the quantum-phase transition upon the systematic variation of the spin-orbit coupling strength. A non-time-reversal symmetry-breaking mechanism of bulk-mediated scattering processes that increase with decreasing spin-orbit coupling strength is proposed as explanation.