In this paper, a new passivity-based technique is proposed to analyze and guarantee the stability of haptics-enabled telerobotic rehabilitation systems where there is a possibility of having more sources of non-passivity than communication delays. In practice, the difficulty of therapeutic exercises should be tuned taking into account the stage of physical disability. However, tuning the difficulty and intensity should not violate the stability of patient-robot interaction. This usually puts conservative prefixed limits on the allowable exercise intensity. In this paper, patient-robot interaction safety is studied in the context of Strong Passivity Theory (SPT). Our goal is to ultimately relax the limitation on the allowable robotic therapies while preserving system stability. The proposed stabilizing scheme does not try to make the entire non-passive component passive. This allows the therapist to have freedom in injecting energy into the system for assistive therapies while ensuring safe patient-robot interaction. In this paper, the case of telerobotic rehabilitation is considered. Experimental implementation and evaluation are presented to support the proposed theory.