Couple of points:
Max HP do not necessarily reset after a long rest. At least, this is not intrinsic to the long rest rule itself (which only regains hit points and half your hit dice if you spent any).
It is true, however, that an effect that drains max HP will also provide you with the means by which they are regained and this is often by resting. For example, the Wraith can drain life, but also provides the means by which it is regained:
This reduction lasts until the target finishes a long rest.
Just note that this quote is from the Wraith's Life Drain ability, not the long rest rule. Other effects that cause loss of max HP may not come back with a rest, but may instead require a healing spell of some kind (Greater Restoration will typically always work) or the sacrifice of a goat under the full moon.
Stat point loss is indeed much rarer in 5th edition than previous editions, but it is not true that it has gone completely. For example, the Shadow drains Strength.
Again, like max HP loss, any effect that drains an ability score will provide some way of getting it back. For the Shadow this is when you rest:
The target dies if this reduces its Strength to 0. Otherwise, the reduction lasts until the target finishes a short or long rest.
You, as the DM, are free to make your item drain Max HP or ability scores as you see fit, and it is up the you to decide how that loss can be recovered. (I would recommend some way of recovering it though, as it isn't fun for a player to feel his character has been irrevocably weakened!).