WotC recently released the Basic Rules for the DM, and with it came a few items like the Amulet of Health:
Wondrous item, uncommon (requires attunement)
Your Constitution is 19 while you wear this amulet. The amulet has no effect on you if your Constitution is already 19 or higher.
The Basic Rules state at the end of Chapter 1, under "Beyond 1st Level":
When your Constitution modifier increases by 1, your hit point maximum increases by 1 for each level you have attained. For example, when Bruenor reaches 8th level as a fighter, he increases his Constitution score from 17 to 18, thus increasing his Constitution modifier from +3 to +4. His hit point maximum then increases by 8.
But it doesn't explain what happens when the Constitution modifier decreases!
My players will soon get the Amulet as a reward, and I fear that they will just pass the item around to increase everyone's max HP; I want to prevent that. Are the HP lost when a character is no longer attuned to the Amulet?