Razor Bob
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A: A razor bob is, simply, a bob haircut that is created using a razor tool. The overall effect is a very soft look without the typical sharp angles created in a bob haircut.
Frankly, I think it might make a nice style for the woman in question, particularly if the cut is styled with some volumizing and lift-producing techniques, as well as being styled to accentuate the smooth curving inherent in this kind of cut.
Remember that with a square face the goal is to create softness and roundedness in order to give the appearance of a more oval face shape.
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See also:
How to cut a blunt bob with bangs and razor texturing
The basics of the bob haircut
How do you razor cut hair into a shag bob?