The quantum field theory for a massless scalar field on a two-dimensional non-singular black hole spacetime with an outer and an inner horizon predicts that there is a non-vanishing probability for a particle localized inside the inner horizon to tunnel out of the black hole. The tunnelling probability monotonically asymptotes to a maximal value that is inversely proportional to the sum of the inverse surface gravities of the inner and outer horizons of the black hole.