A woman with a beard most likely has a malfunctioning?

I wouldn't use the Word "malfunctioning", I would use the Word "imbalanced" so the question would be "A woman with a beard most likely has an imbalanced:

-thyroid

thyroid helps balance hormones and women growing a beard has too much testosterone, too little estrogen or both. This is also caused by natural drop in estrogen through pre and post menopause.

Imbalances can also be caused by overweight, excessive exercising, chemo (which affects the thyroid) and a number of health issues.

If facial hair growth started suddenly or is happening without some of these other possible causes, it's time for a Dr. visit and lab tests to measure thyroid function and hormone balance.