They can.
I'm talking about amber, but not only, there have been occurrences of hair in fossils.
Plus, if the cells are preserved well enough, even if there's no actual hair anymore, we can still determine where they were.
However, this is true, we can't rule out this possibility, because it would require to have a specimen where the entire body is extremely well preserved, and even then, we couldn't be sure about the length. Unlikely though!
I'm talking about amber, but not only, there have been occurrences of hair in fossils.
Plus, if the cells are preserved well enough, even if there's no actual hair anymore, we can still determine where they were.
However, this is true, we can't rule out this possibility, because it would require to have a specimen where the entire body is extremely well preserved, and even then, we couldn't be sure about the length. Unlikely though!