Hello. If the wisdom teeth has not erupted properly, it will have to be removed by surgical method, irrespective of how much tooth is remaining.  You will have some pain and swelling, which can be controlled by medicines. If you delay for a long time you may end up having more infection and pain.

Third molars or wisdom tooth are removed under local anesthesia ...when the tooth is half broken .. remaining tooth and roots are to be removed surgically , usually overlying gum and minimum amount of overlying bone is usually removed to facilitate the removal of wisdom tooth .. total procedure will be under the coverage of antibiotics and local anesthesia so you will not experience any pain.. u will experience slight discomfort which can be managed by the analgesics ...