My cousin has stage 4 osteosarcoma, what are her chances of survival for one more year?

It depends: It depends on the size and number of the nodules in the lung and if they can be removed surgically or not. If they can, chances of long term survival are better. If the cancer had spread to other bones, the prognosis is worse. But in general, nobody knows how long any of us has to live. Follow the oncologist's recommendations to maximize chances of survival.