Obviously if the density of the object is smaller than the density of water it would not sink at all. But I was thinking that, even if the density of the object is greater than the density of water, maybe the object would not sink to the bottom of the ocean floor because the pressure of the water increases as the depth increases. So maybe after a certain depth the pressure of the water would become great enough to counterbalance gravity and push back the object towards the surface.
And if the object would not completely sink to the bottom of the ocean floor, at what depth would the object stop sinking and stabilize itself (depending on its density)?