Can a nearsighted person become farsighted?
It is indeed quite possible to have both nearsightedness and farsightedness in the same eye, and at the same time. While this sounds strange, it is quite common -but it does matter how you are using the term "farsighted."
Nearsightedness (myopia) is where distance vision is blurry but near vision is usually good (both without glasses). Myopia is typically caused by the eyeball growing too large in childhood: the default focal point is somewhere up close instead of off at a distance as is normal. When people say 'farsighted," they are almost always referring to Presbyopia: the age-related loss of the ability to pull one's focus up close such as for reading texts on a cellphone. Presbyopia is caused by the gradual, age-related hardening of the natural lens of the eye and not by how big or small the eye is. Presbyopia (by itself) only affects vision out to about arm's length, not at a distance. Being nearsighted can be very useful when we reach middle age and Presbyopia sets in, because by taking off your glasses you can now see up close by using that myopic default focal point no matter the Presbyopia or how hard your natural lens might have become.