In the 12 dependent links, grasping and clinging (links 8,9) causes becoming (link 10) which in turn cause birth, aging and death (Links 11 and 12). But grasping and clinging are caused by consciousness, name and form, 6 senses, contact and feelings (links 3,4,5,6,7). The immediate cause is feelings of negative, positive and neutral. Consciousness is cause by karmic formations (link 2) and it is cause by Ignorance (link 1). At death if we are still ignorant, the cycle of uncontrolled rebirth continues.
So, the root cause is ignorance but grasping and clinging is what keep us in samsara. To rid one of these cause, one practices to rid one of grasping and clinging by accumulating the merits and wisdom to see the ultimate truth that leads to Liberation (non existence of the self) and Omniscience (non existence of others/phenomena).
Non existence do not refer to total non existence by the mode of existence is based on dependent arising ie in the form of cause and effect and that things and in flux and constantly changing based on cause and conditions and what we see as existing is ever changing. That is no use to be attached to these events.