A dental abscess will not heal without treatment. While the toothache may subside once the dental abscess damages the pulp inside your tooth, it does not mean that the infection has gone away. The dying of the pulp causes the nerves to stop functioning, thus making them unable to feel the pain. The bacteria will continue to spread and deteriorate the surrounding tissue.
If you have any symptoms of a tooth abscess, it is important that you make an appointment with a dentist as soon as possible, even if the pain has gone away.