We consider systems modeled by a differential inclusion subject to impulsive, set valued state resets. We study existence of solutions for this class of systems and derive conditions for a set of states to be viable. From the point of view of hybrid systems, of central interest is the fact that the class of systems and the solution concept considered allow any finite number of left and right accumulation points of the impulse times; in other words, very complex Zeno type behaviors. The results are demonstrated on simple examples that exhibit such behaviors.