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If one inserts an ED disk (Extra-high Density disk) into a floppy drive, which supports sizes only up to HD (High Density), how does it cope with ED?

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It doesn’t, at least not in any particularly useful way. Because of the position of the density sensor cut-out on ED floppy disks, they’re detected as 720K floppies by HD drives. Their contents can’t be read, and they can’t be used, as explained in Michael Karcher’s answer.

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It won't work reliably at all. The magnetic properties of ED media are very different from the magnetic properties of HD or DD media.

On both HD and DD media, the magnetization is "in-plane" or "longitudinal", which means that the information is encoded by some areas of the disk being magnetized in rotation direction and other areas are magnetized contary to the rotation direction. In either case, the field from north to south is parallel to the rotation direction. The coating is designed such that this kind of magnetization is stable.

On the other hand, ED disks use "perpendicular" recording. The magnetic north pole is on top of the coating, near the head, and the south pole on the bottom of the coating, at the plastic disk (or the other way around with the north pole at the plastic layer and the south pole on top of the metal layer). The coating is unable to keep longitudinal magnetization, as it is written by HD or DD read/write heads. The field will slowly (or not so slowly) tilt into perpendicular direction, loosing the actual information.

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