EAGLE went beyond PCB size limit?!

Looking at that picture, there seems to be a dimension line drawn, but it's well outside of where your ground plane is. And the traces are well within that dimension line. I see four holes, two of them within your ground plane, and two of them outside, in the same area that you have the text written. Eagle WILL route traces within dimension lines, and if they are drawn larger than what you expect the board to be, it will gladly put traces there.