Preprint. Instead of assuming perfect foot contact, this framework incorporates slipping directly into a model of bipedal walking. Virtual nonholonomic constraints regulate stance-foot tangential velocity alongside the holonomic constraints that define the gait. The closed-loop model combines continuous motion with discrete impacts. A nonlinear feedback law enforces the constraints, while a Poincaré-map analysis characterizes stability of periodic walking. Numerical examples illustrate stabilization when slip occurs.