It's not normal for cats claws to fall out unless they've injured the claw.
If you've seen a "claw" lying on the carpet etc, and the cat has not injured his/her foot, then what you're probably seeing is the claws sheath (outer layer of the claw but not the claw itself). When you see your cat chewing on it's claws it is often trying to dislodge the old and worn sheath. Once it falls off there is a brand spanking new one right underneath. The sheaths look like claws but it is only the shell of the claw. If kitty is not limping or bleeding, then you can assume that it's just a claw sheath on the floor, and not your kitty losing it's claws in their entirety.
If you've seen a "claw" lying on the carpet etc, and the cat has not injured his/her foot, then what you're probably seeing is the claws sheath (outer layer of the claw but not the claw itself). When you see your cat chewing on it's claws it is often trying to dislodge the old and worn sheath. Once it falls off there is a brand spanking new one right underneath. The sheaths look like claws but it is only the shell of the claw. If kitty is not limping or bleeding, then you can assume that it's just a claw sheath on the floor, and not your kitty losing it's claws in their entirety.