Astrophysics question: Are zero braking distance collisions and infinitive forces possible?

Whenever we hit the brakes while driving, it will take some time and distance until we come to a stop. Even during a head-on collision the crumple zones lead to a small, but non-zero braking distance. The same applies when we trip and hit our head on a hardwood floor. Even when two metal spheres collide, their electron clouds prevent an instantaneous stop. The braking distance is never zero.

Now consider two “small” neutron stars with their combined mass not being heavy enough to form a black hole.

Suppose they are on a collision course. It’s rare, but it can happen (on a cosmic time-scale).

When the collision occurs, there are no electron clouds to act as a buffer, no electromagnetic forces that cause a non-zero braking distance. All there is are neutrons, tightly packed. Even the nuclear forces are powerfully attractive, not repellent.

Would this lead to an instantaneous stop of both stars?
Is there an infinite force and infinite deceleration involved?
Would the collision destroy both neutron stars creating numerous smaller fragments?
Or would a single new neutron star with the combined mass be formed?