All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The Muslim woman is obliged to cover her hair as long as it is attached to her head; Allah, the Exalted, says (what means): {O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves (part) of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful.} [Quran 33:59] If her hair is detached from her head, she is not obliged to cover it. Accordingly, she bears no sin if a non-Mahram (marriageable) man happened to look at it. However, scholars held that it is recommended to cover the hair or other parts that are detached from the body, such as nail clippings, because these are parts of the body of the human being whom Allah has honored; Allah, the Exalted, says (what means): {And We have certainly honored the children of Adam and carried them on the land and sea and provided for them of the good things and preferred them over much of what We have created, with (definite) preference.} [Quran 17:70]
Al-Haafith Ibn Hajar wrote, “Our scholars held that it is recommended to bury them because they are parts of the human being.” [Fat-h Al-Baari]
It should be noted that scholars held different views regarding the ruling on a non-Mahram man looking at the parts detached from a woman's body, including her fallen hair. some held that it is permissible, others held that it is impermissible, and others differentiate between what is detached during her lifetime and what is detached after her death.
Allah knows best.