I have seen this once in the past and again it was a car which did not have a lot of use. We came to the conclusion after a careful inspection and a lot of debate that when the car was parked up the discs would be hot( they do get VERY hot), then, being a frosty night they had sweatedc ausing moisture on the disc to freeze. The moisture had worked it's way between the friction material and metal backing part of the brake pad, frozen and, at least partly, forced the material away from the metal so as soon as the car moved it dragged the material away from the metal,at which point it is very possible for it to fall to the floor. Obviously the piston then has to travel further before it meets the disc(therefore needing more pedal travel). When it eventually met the disc it was the metal backing which hit the disc(hence the grinding noise). Sorry this answer became a bit of a saga but it needed all of it to make sense, I just hope it made as much sense to others as it did to us.