There are several possible causes of brown toenails.
Repetitive trauma (like running in a shoe that is too small, for example) can make the area under the nail bleed, causing a subungual hematoma. Also, certain myotic infections (fungal infections) can cause the underside of the nail to gather fungal debris of a brown or clack color. Women of color may get dark stripes or dark areas in their nails that are completely normal.
It’s hard to say whether the fact that your client picked off the nail is the cause of the discoloration without seeing it.
I don’t think a person could comfortably pick off her own toenail unless it had been injured previously or there was a fungal infection under the nail, causing the nail to lift off the nail bed.
If there is crumbly nail debris under the nail that is brownish, it may be a fungal infection. I have noticed that the darker fungal infections can be malodorous, so if it is brown and it has an odor, it is probably a fungal infection.