It is called extended hyponychium and it is often present on people with long fingernails and is generally not a problem. It can be a problem when it is necessary to cut down the nails and you cut into the hyponychium. And you should not use any pointed or metal implement to clean under the nail. For the client, applying cuticle oil regularly and gently pressing it back (with a finger, never a metal implement or pointed stick) will help. Also, gently pressing it back after a shower/bath/dishwashing is helpful.
In this case, however, I think it may be a problem because of the onycholysis on the neighboring nail that Trinity observed. It might be worth having her keep her nails shorter for a while, applying cuticle oil (tea tree oil seems to work especially well) and, of course, avoiding any trauma to the nail.