Human bodies don't lose much buoyancy at all with depth. Tissues are mostly water and don't compress; the air spaces in the body are small, with the exception of the lungs. But the magic of the scuba regulator is that it delivers air at the same pressure as the water where you are, and if the lungs are full of that pressurized air, they don't compress!
So what DOES lose buoyancy? Anything you have with you that has gas in it and doesn't have a rigid container. That means the air bladder of your BC, any padding you have on anything, and your wet or dry suit. Now, the BC bladder and dry suit are kind of like your lungs -- you can fill them with pressurized air and stop the compression. But your padding and your neoprene don't have that option, and they do compress. Thick wetsuits can lose quite a bit of lift. In the days before BCs were used, this meant the diver had to provide the additional lift by swimming -- a diver in thick neoprene in those days was rarely actually neutral.
The BC, or "buoyancy compensator" was designed precisely to solve this. By adding air to the bladder, you COMPENSATE for the loss of buoyancy that your wetsuit has experienced with depth. That way, the diver can remain neutral, which means he can also stay still. That's nice if you want to remain in place and watch octopuses fighting over a den space, as we did for quite a while on our last dive.
Of course, if you are using your BC to compensate in this way and it fails, you have a problem. You may need to swim up, as people did before BCs. If you are wearing very thick exposure protection, this may be somewhat difficult, which is why divers are advised to keep at least some of their lead weight ditchable.
So the short answer is: If your equipment is working and you are using it properly, there is no depth where you plummet to the bottom. If you have a gear failure, you will have to provide additional lift from your fins, or reduce the degree you are negative by jettisoning weight.