  We consider a class of quasiregular singularities characterized by points
possessing two future-directed light cones and two past-directed light cones.
Such singularities appear in the $1+1$ trousers spacetime and the
Deutsch-Politzer spacetime. We argue that these singularities are relevant for
describing the end point of an evaporating black hole, and show that a class of
emergent Lorentz signature theories can provide a microscopic description for
these singularities.
