Phase segregation of multicomponent lipid bilayers leads to, under phase-coexistence conditions, domain formation, featuring delimitation by essentially one-dimensional borders. (Micro-)phase segregation of bilayers is proposed to influence the physiological behaviour of cell membranes and provides the driving force for lipid-raft formation. Experiments show a maximum in the electrical-conductivity of membranes at the phase-transition point, which has been conjectured to arise from border-nucleated transmembrane-conducting defects or pores. However, recent electroporation experiments on phase-segregated bilayers demonstrate electro-pore detection in the liquid disordered phase (Ld), wherein they diffuse over macroscopic periods without absorption into the liquid ordered phase (Lo). Here, we scrutinise transmembrane-pore formation via molecular dynamics simulations on a multicomponent phase-segregated bilayer. We find that pores created in Lo domains always migrate spontaneously to the Ld phase, via 'recruitment' of unsaturated lipids to the pore's rim to transport the pore to the fluid phase under a large stress-field driving force. Once in Ld domains, pores migrate towards their centre, never returning or pinning to Lo. These findings are explained by thermodynamics. By comparing the free-energy cost for creating pores in the bulk of Ld and Lo membranes, and in the phase-segregated system, we show that it is always more energetically tractable to create pores in Ld domains, independent of the pore size.