Can my mother sue due to a non-working escalator that caused her to brake her jaw?

Please select Los Angeles as your geographic location, as mentioned earlier. That will elicit responses from CA lawyers.

She could but she has virtually no chance without a personal injury attorney!

I would suggest that you consult a California licensed attorney to see if your mother has a viable lawsuit. If I was investigating this case I would want to know more about the malfunction to the escalator. For example was it malfunctioning before your mother used the escalator or did it malfunction while she was on the escalator. Also, were there any warnings regarding the status of the escalator. I would suggest you pursue this matter as soon as possible because there is a better chance of contacting witnesses and locating repair or safety reports concerning the escalator. Best of luck.