My chainstays have been eaten by rust, can something be done?
The only thing that can be done to save the frame is to have patches welded over the holes. You would need the expertise of a professional welder to get it done properly so that the frame is made structurally sound.
Unfortunately, you may find that this repair is more expensive than simply finding a similar replacement bike or frame. The welding repair job will involve removing the wheel, crank, bottom bracket bearings and other components to in the area to be welded. The frame will need to be repainted as well of course.