We investigated global integration (wrap-up) processes at the boundaries of musical phrases by comparing the effects of well and non-well formed phrases on event-related potentials time-locked to two boundary points: the onset and the offset of the boundary pause. The Closure Positive Shift, which is elicited at the boundary offset, was not modulated by the quality of phrase structure (well vs. non-well formed). In contrast, the boundary onset potentials showed different patterns for well and non-well formed phrases. Our results contribute to specify the functional meaning of the Closure Positive Shift in music, shed light on the large-scale structural integration of musical input, and raise new hypotheses concerning shared resources between music and language.