I found the answer while trying to write the question. Hopefully this helps others
We usually say that hair is “made” of a protein called keratin—that’s a bit of a simplification. As hairs become part of the shaft, they undergo a process called keratinization, in which they become filled with keratin. So, technically, instead of being made up of pure keratin, hair is made up of dead cells that are filled with and surrounded by keratin.
Source
I'd say some visualisation would be helpful, please add a new answer or propose edits to this answer