A black hole without an event horizon is a naked singularity[1], a concept in theoretical physics resulting from looking at the mathematical equations that describe black holes and observing that the event horizon's radius becomes undefined at certain angular velocities[2]. It's not clear if it can exist in reality.
AFAIK (not a physicist), gravitational force of a specific object (as a function of distance) cannot be discontinuous, can it? It's definitely not under the classical F=G(M1)(M2)/r^2 equation. Force can't be discontinuous unless mass changes discontinuously or space changes discontinuously. But I don't know if there are extreme conditions (and a naked singularity might qualify) where that equation breaks down, or is thought to break down?
[0] to support the movie Interstellar, several people worked on an accurate rendering, based on known physics, of a rotating black hole: https://astronomynow.com/2015/02/14/interstellar-technology-...
[1] https://en.wikipedia.org/wiki/Naked_singularity
[2] https://physics.stackexchange.com/questions/147034/rotating-...