We predict that broken-gap InAs/GaSb core/shell nanowires, when operating in the topological insulating regime, undergo a collapse of the hybridization gap under the application of a transverse electric field. We perform predictive, self-consistent k p calculations for realistic nanostructures and show that a gap closure occurs at two Kramers-related, massless Dirac points at a critical value of the field in the V/,a range. An analysis based on the Bernevig-Hughes-Zhang model shows that the newly predicted semimetal phase stems from the cancellation between the kinetic electron-hole hybridization and the spin-orbit interaction, which is controlled by the external field. Remarkably, the so-called end states-midgap states localized at the terminations of a finite-length nanowire in the inverted regime, analogously to spin Hall edge states-are supported only below the critical field, and suddenly disappear as the system is driven through the semimetal phase, eventually evolving into trivial surface states. This abrupt disappearance exposes a nontrivial transition in one dimension driven by spin-orbit coupling.