With no air in the brake system, (because it has been properly bled) if the pedal will go to the floor when pressure continues to be applied to the brake pedal and there are NO external brake fluid leaks in the system such as via a deteriorated flexible brake hose, then the problem will normally be with a worn brake master cylinder (MC) . Heavy wear in the internals of the brake MC , (the pistons and bore), will cause the problem you have. This is a common problem on older car with lots of miles on them where the brake MC has had a great deal of use and where the brake fluid has not been changed as frequently as it should be.
If the MC was in good shape, you have no air trapped in the MC or in the brake lines, and the brake pedal goes to the floor then you would have an external fluid leak as the leak releases pressure in the hydraulic system as you continue to apply it with the brake pedal.
If the brake MC has to be replaced (or is otherwise removed for a repair work on the car) it is imperative the air is bled out of the master cylinder itself when the new MC is to be installed (or the original is replaced) and there is a procedure for this. If the brake MC unit is not bled of air, then applying the brakes will compress the air in the MC unit and you will get a low pedal. (Bleeding the brake lines on the car does NOT remove any air trapped in the brake MC due to failure to bleed the MC itself).
Brake Master Cylinder
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