Offset responses in auditory processing appear after a sound terminates. They arise in neuronal circuits within the peripheral auditory system, but their role in the central auditory system remains unknown. Here, we ask what the behavioral relevance of cortical offset responses is and what circuit mechanisms drive them. At the perceptual level, our results reveal that experimentally minimizing auditory cortical offset responses decreases the mouse performance to detect sound termination, assigning a behavioral role to offset responses. By combining in vivo electrophysiology in the auditory cortex and thalamus of awake mice, we also demonstrate that cortical offset responses are not only inherited from the periphery but also amplified and generated de novo. Finally, we show that offset responses code more than silence, including relevant changes in sound trajectories. Together, our results reveal the importance of cortical offset responses in encoding sound termination and detecting changes within temporally discontinuous sounds crucial for speech and vocalization.