I can't speak about nails and hairs specifically, but directional cell growth is common in nature.
In plants, for example, cells replicate primarily at the tip of a bud, which allows branches to lengthen directionally rather than grow out in all directions. The plant produces growth hormones, which are transported upward throughout all branches until they reach a dead end. When they reach a dead end, they stop moving and just sit there, which causes the cells at the dead end to have a greater exposure to these growth hormones. These cells bathe in growth hormones for so long that they pass the hormone-exposure threshold that triggers cell replication.
In plants, for example, cells replicate primarily at the tip of a bud, which allows branches to lengthen directionally rather than grow out in all directions. The plant produces growth hormones, which are transported upward throughout all branches until they reach a dead end. When they reach a dead end, they stop moving and just sit there, which causes the cells at the dead end to have a greater exposure to these growth hormones. These cells bathe in growth hormones for so long that they pass the hormone-exposure threshold that triggers cell replication.