Sadie doesn't leak, and she is only a puppy... I do wipe both my babies because when they go they are wet there. I guess if you didn't wipe them they may drip a bit??? I doesn't sound like pee to me. Why would it be white? And it would really smell after a while.
Could it be drool? that might be white when it dried. It might not have to bad an oder.
I would put a blanket down for them to lay on.