When can a classifier be omitted? E.g. in 一女子跟着自己的包进了安检机
IMO, 一女子 can mean "there's one woman"， 有一名女子 or 某女子. The measure word can be omitted only when the number is one 一. We don't usually say 两女子，三女子， and we say 两名女子，三名女子 instead. 

More examples: 一小孩 == 一个小孩; 一老人 == 一个老人; 买一玩具 == 买一个玩具; 

However, I wouldn't suggest such omissions since the rule might not work very well for all the noun words. We'd better add the measure word and it will work all the time.