I know in Ancient Chinese there often was no classifier. But sometimes I notice the same phenomenon in modern Chinese. Today I heard the sentence:
For which words is such a usage idiomatic? What decides when to omit the classifier?
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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.
Usually we do not omit the classifiers. The sentence in your example, I guess, probably comes from a news title, where brevity matters so there may be omission of the classifiers. But it's also correct to replace it with 一名女子 in your example.
Also, omission can happen in oral Chinese. For example I may say, 饿死我了，我中午就吃了一苹果。(I'm starving, I only ate an apple for lunch.) In this case (oral language), I don't think there's any restriction on which classifiers are allowed to be omitted.