Brake pads sink to the floor

Okay, when does it sink to the floor? Engine running, engine off? Does it seem to stop but the pedal keeps going down? How fast does it sink? Are you losing brake fluid?
You say everything has been checked, but has anything been replaced? Was anything done just before this started, like new brakes or line or what?

Sinking pedal is the result of fluid leaking, either external through a caliper/wheel cylinder, pinhole in a brake line, damaged rubber line (acts like a ballon and expands then when you let off it pushes the brake fluid back into the system), or internal leakage in the master cylinder or inside the booster if the master is leaking past the end seals.
Generally if you have a sinking pedal and it sinks regardless of engine state and you do not have fluid loss it is a bad master cylinder. The internal seals are damaged and letting the fluid get past them.
If the pedal does not sink with the engine off then check the booster for fluid, you can usually see dampness inside the booster vacuum line if this is the case.
If you have fluid loss you have an external leak. I have seen them leak from a pinhole and spray out like a spray nozzle without leaving any fluid on the vehicle.

These are all different from a spongy pedal, that feels like you are stepping on a balloon or air filled ball.