Does this item exist?

A -20 HP wand ... or any minus hp wand for that matter

Negative health items are limited to offhands only.

And the highest offhand is -50, you get that from a quest in Ascalon. Or just pay like 2-3k for it in droks.

This off hand is also used in the making of 55 monks

ive had a -20 HP offhand, sold for a few k's but like said before, there are no main hand negative health items

there is/was a -20hp axe. it was nerfed but noone is sure if it was removed or is just really really rare

the -20 monk off hand is available in pre-sear as a reward, besides the ceste, i dont know of any other -health items

You can also get them as drops.

We had a -20 hp offhand drop from a Shiverpeaks chest.

If you run a 55 build and you die and get rezed, you will have 1 health. At this point, you switch the -50 offhand, for the -20, and you will be able to continue with somewhere around 30ish health.

I have a couple of -20's, and they have all been drops.