How can I stop my cat losing claws?

I have a cat that is very playful, even though she is almost nine years old. We have carpet in our house that has a lot of depth to it, and sometimes when she plays she hooks her claws in the carpet. I try to get her out, but being in pain she doesn’t let me near her. I find 1–2 claws a week lying on my carpet. How can I stop this happening? Preferably without her losing this playfulness.