You wouldnt need a written deed, just proof you were born there and it is multi-generational. Citizenship is based on where you are born, not what you own.
But while citizenship should be automatic ownership of the plot of land might be debatable... IF they can show they were born there and dont have a deed, then someone else would have to prove they had a deed that pre-dated their birth and living in that home. The earlier deed wins, but absense of a physical deed it would default to whoever can show they were born and raised there first (since no owner can otherwise be identified).