The onset of low-velocity collisions in vibro-impacting systems induces instabilities in the system dynamics that, when not checked, may result in sudden, and unanticipated discontinuous transitions between distinct steady-state responses. This paper illustrates this phenomenology in an example system that includes dry friction. Here, the instability is associated with the zero-velocity contact of an oscillatory unilateral constraint and a stationary mass suspended through a preloaded spring. The analysis summarizes observations on the passive response of the mass under variations in the oscillation amplitude of the constraint. A control strategy is subsequently shown to successfully suppress the instability. The paper concludes with suggestions for applications of this phenomenology as well as a description of similar observation in mechanical systems with or without friction and with rigid as well as compliant contact.