Historically, FMJ bullets are made with an exposed lead base. The base of the copper cup used for the jacket becomes the nose of the bullet. Even FMJ rifle bullets generally have an exposed lead base.
Hollow points, on the other hand have the exposed lead at the nose of the bullet. the base of the jacket cup becomes the base of the bullet.
In recent years, companies have made some totally enclosed full metal jacket bullets by placing a copper disc at the base of the bullet. One of the reasons is to minimize lead exposure at indoor ranges.
Plated bullets are completely enclosed due to the plating process.
As FROGO207 said, if the lead cannot touch the rifling, leading is not an issue.