The concepts of G-passivity and G-passifiability (feedback G-passivity) are introduced extending the concepts of passivity and passifiability to nonsquare systems (systems with different numbers of inputs and outputs). Necessary and sufficient conditions for strict G-passifiability of nonsquare linear systems by output feedback are given. Simple description of a broad subclass of passifying feedbacks is proposed. The proofs are based on a version of the celebrated Yakubovich-Kalman-Popov lemma.