In theories where physics depends on a global foliation of space-time, a black hole’s horizon is surrounded by an “eternity skin”: a pile-up of spacelike leaves that in the far-out region cover all times from the start of collapse to future eternity. Any future foliation-dependent change in the laws of physics would be enacted in this region and affect the last stages of collapse toward black hole formation. We show how in some cases the black hole never forms but, rather, bounces into an explosive event. There is also a nonlocal transfer of energy between the asymptotic Universe and the formed black hole precursor, so that the back hole (if formed) or the exploding star (otherwise) will have a different mass from what was initially thrown in. These last matters are generic to nonlocal theories and can be traced to the breakdown of the local Hamiltonian constraint.