High-gain PID position control, which is widely used with robots having complex dynamics, involves some risks in cases of abnormal events, such as unexpected environment contacts, temporal power failures, and wrong position commands from a higher-level controller. We previously proposed a proxy-based sliding mode control (PSMC) scheme, which is an extension of PID control that ensures slow, moderate, overdamped recovery from a large positional error at abnormal events without sacrificing tracking accuracy during normal operation. Its weakness is that the velocity is not bounded. This paper proposes a velocity-bounding PSMC (VB-PSMC) scheme, which is an extension of PSMC to impose an arbitrary magnitude limit on the velocity. The VB-PSMC method can be used as a lowest-level position servo that is safer than PSMC and much safer than conventional PID control. The advantage of VB-PSMC was demonstrated through implementation experiments.