The anti-debeading edge (also called hump) is an embossed edge inside the dropwell that keeps the bead in place. When the inflation pressure isn’t sufficient, the bead could run through or slip in the dropwell causing the sudden collapse of the tire resulting in a loss of control of the vehicle: this is the so-called debeading. An anti-debeading edge (or hump) is needed specifically to avoid that such such events will happen, by not allowing the bead to slip over the dropwell even when the inflation pressure is low or none.
In case of a puncture on a tire with tube (tube type) the loss of pressure is almost istant and, in the absence of hump, the tyre could suffer a sudden beading with dangerous consequences on the vehicle balance. With a tubeless tire the loss of pressure is usually slower and gives enough time to the rider to stop, but without an anti-debeading rim is not recommended to keep riding because when the air pressure becomes very low, it is possible that the beading will occurs with a consequent deflation of the tyre.
The anti-debeading rim is necessary for tubeless conversion, but it is also recommended when using air chambers.