A mass–spring–damper slider excited into vibration in a plane by a moving rigid belt through friction is a major paradigm of friction-induced vibration. This paradigm has two aspects that can be improved: (1) the contact stiffness at the slider–belt interface is often assumed to be linear and (2) this contact is usually assumed to be maintained during vibration (even when the vibration becomes unbounded at certain conditions). In this paper, a cubic contact spring is included; loss of contact (separation) at the slider–belt interface is allowed and importantly reattachment of the slider to the belt after separation is also considered. These two features make a more realistic model of friction-induced vibration and are shown to lead to very rich dynamic behavior even though a simple Coulomb friction law is used. Both complex eigenvalue analyses of the linearized system and transient analysis of the full nonlinear system are conducted. Eigenvalue analysis indicates that the nonlinear system can become unstable at increasing levels of the preload and the nonlinear stiffness, even if the corresponding linear part of the system is stable. However, they at a high enough level become stabilizing factors. Transient analysis shows that separation and reattachment could happen. Vibration can grow with the preload and vertical nonlinear stiffness when separation is considered, while this trend is different when separation is ignored. Finally, it is found that the vibration magnitudes of the model with separation are greater than the corresponding model without considering separation in certain conditions. Thus, ignoring the separation is unsafe.