Embedded Jewelry is rather uncommon and is easily prevented with a little bit of attention to your piercing. If you are pierced with or put in jewelry that is too small, it can become embedded in the skin.
If this is happening due to swelling after the initial piercing - do not panic. Take 2 anti-inflammatory pills every 4 hours - generic Ibuprofen is the most effective. The swelling should subside in 12hours. If you notice the piercing pulling in during this period, wash your fingers and gently push the piercing free from the wound. This may be uncomfortable or painful but will prevent the jewelry from becoming embedded.
If this happens overnight, it may require a more forceful push to remove the jewelry from the wound.
This type of reaction is extremely common in nipple piercings and nostril piercings with studs.
If the swelling does NOT recede in 12 hours, contact your piercer and go get them to change the jewelry to a longer piece.
Oral piercers like lip and tongue piercings nest in the tissue during healing, this is normal, lightly push them free and move them periodically. If your piercing has gone into your skin more than 1/4 inch - contact your piercer.
In the event that the tissue completely grows over the jewelry and you or your piercer cannot push it back through the surface, you must seek medical attention as soon as possible.