The phrase "brink of abyss" describes a situation that is perilously close to a disastrous outcome. If you're looking for synonyms that capture this sense of imminent disaster, you might consider "precipice," "verge," or "edge." These words all suggest a dangerous proximity to the unknown or the uncontrollable. Other options could include "cusp," "threshold," or "abyssal depth." Each of these words captures a slightly different nuance of the looming disaster at hand, but all suggest that danger is lurking just beyond the horizon. Whether you're describing a personal crisis or a global catastrophe, these synonyms can help you convey the gravity of the situation.