Nails do not stop growing. Some nails appear to stop growing when in fact they may grow at an abnormally slow rate. In addition, if they grow out only a certain distance on the nail bed and no farther it is not because there is no growth; rather, some people have nails that are more fragile than normal. They break readily and do not grow past the nail bed.
There is no known way to make nails grow faster or longer; however, intake of multi-vitamins, and minerals along with biotin supplements has been reported to help some people. Extensions may be worn if your client is not allergic to the product. However, a periodic rest without any nail products may also be helpful.
I cannot explain the loss of the fiberglass nails, but I do suggest a dermatologic evaluation if there is a nail bed problem.