Beyond that, we get nonsense. The initial-value problem for the classical stiction damped oscillator is a famous ill posed problem in nonsmooth analysis. As a hybrid system it is also ill posed. But, there are arbitrarily close generically well posed problems. Hybrid systems are not dynamical systems.
Hybrid systems can exhibit much more complicated behavior than dynamical systems can.
In fact, there is a very special kind of bifurcation associated with hybrid systems. A second-order position servo with a hysteretic controller cannot be described by differential equations. Conf. , 1107-1112.