Thank you for your question, and please forgive me for writing back in English.
From the description of your family member's symptoms, it appears that he or she may be suffering from onycholysis (空甲症), which can have many causes, including onychomycosis (灰甲). The best thing to do is to see a family doctor or dermatologist so that a definitive diagnosis can be made, and appropriate treatment can be given.
Hoarseness is a symptom that can have many different causes. If there is no obvious explanation for it and if it does not go away after simple treatment, a more thorough investigation may have to be carried out, preferably by a throat specialist.