Rebreathers have a large interior gas space - the "loop", which includes the breathing hoses and mouthpiece, the counterlungs and the canister that contains the scrubber. A diver would be positively buoyant at the surface with gas in the wing (not part of the loop).
Normally, if a diver on the surface takes the mouthpiece out of their mouth, they close the "dive/surface valve" so that no water can get into the loop. If the diver loses consciousness on the surface, the mouthpiece would fall out of their mouth with the DSV open, and the entire loop would flood, making it very negative, and causing the diver to sink. This is a well known scenario in rebreather accidents.