This post refers to 5th Edition, and you can read information about Demons within the 5th Edition Monster Manual on beginning with page 50.
Demon lords and princes sometimes maintain their vital essences in small containers. Their life force or soul are at once protected and yet still vulnerable if some other creature would gain control of the amulet. Possession of such a powerful item is dangerous. As discussed in the 5th edition Monster Manual, characters can destroy the amulet and trap the Demon within the Abyss for a short amount of time. However, some characters might keep the amulet in order to hold some power over the Demon.
If a Demon’s Amulet is removed from its normal storage area, the Demon Lord it belongs to becomes aware of the situation almost immediately. The Demon will stop at nothing to recover this priceless item. Some wise characters may try to coneal themselves from the Demon, but chances are that these ancient monsters will seek out the thief sooner or later.
A character who has possession of a Demon Amulet runs the risk of attracting the attention of other Demons and Devils as well. The Blood War is ongoing, and a Demon has many allies and enemies. While a character has a Demon Amulet, the chance of encountering a Demon or Devil is doubled. This encounter could go in a lot of different ways as the enemy or ally confronts the character and attempts to retrieve the Amulet for itself.
A Demon Amulet is a powerful and dangerous thing. Those who seek them should tread carefully.