It is likely that the ring would collapse.
Note that the earth is not a perfect sphere. Also, as per laws of gravity, the closer the object to the earth’s center, the object’s gravitational pull is then increased.
This means that different sections of the ring can be affected by varying degrees of gravity. If you remove the supports, assuming all at once, the ring will be pulled towards the center of the earth and parts of it will be pulled faster and with more force than others.
Considering the mass of the earth and its gravitational pull, the ring will more likely break.
Science fiction writer Larry Niven actually envisioned a similar cosmic megastructure, the Ringworld in his novels. In his imagination, however, the ring is a world built around a star. The Ringworld is kept in a position where it is equidistant from the star at all points.
Newton? Einstein? The controversy surrounding gravity theories continues, check out the discussion at Phys.org.
Discover how you turn gravity into light, featured on ScienceAlert.com.