Final answer:
The liver has a close relationship with conditions of the nail, as it produces proteins like keratin and filters toxins that can affect nail health.
Step-by-step explanation:
The organ that has a close relationship with conditions of the nail is the liver. The liver plays a crucial role in maintaining the health of the nails by producing proteins, including the protein keratin, which is the main component of nails. Additionally, the liver is responsible for filtering toxins from the body, and any liver dysfunction can lead to nail abnormalities.