If you are on the verge of something or come to the verge of something, you are very close to experiencing it.

on the verge of collapse/success/tears/death/disaster/war 濒于崩溃／接近成功／差点流泪／濒临死亡／濒临灾难／处于战争的边缘

Her husband's violent and abusive behaviour drove her to the verge of despair. 她丈夫的暴力和虐待行为将她逼到了近乎绝望的境地。