A firestopping sleeve positionable usually in walls which is self-adjusting and includes a sleeve defining an access corridor extending longitudinally therewithin with at least one firestopping pad positioned therein. The sleeve has an access corridor extending therethrough for receiving wall penetrating cables which are firestopped therearound by the pad. A projecting block is attacked to the pad for providing self-adjusting and sealing capability of the device, to prevent air or smoke leaks around the cables.