After landing, the aircraft was backtracking along the runway when the nosegear collapsed. The pilot reported that at the time of the collapse the aircraft was moving at about 4 knots as it was slowed to take the turn into the apron. The nosewheel had become completely detached, allowing the oleo forks to contact the ground. A nosewheel bearing had seized from lack of lubrication. This had caused the axle to spin in its oleo support eyes. One support eye had failed because of the heat generated, and the other failed in overload, allowing the nosewheel to detach.