If a intellect devourer targeted a creature in battle wearing the headband of intellect, could would you say that if they dropped their intellect to 0 that the item would just stop being magical but they would still have their intellect left over. Like an initial shield that gets destroyed

RAW I'd say you're immune since the headband says your intelligence is always 19 while wearing it. So as soon as it drops to 0, it immediately becomes 19 again. This might be a bit powerful, but I think it isn't really significant since they are very situational.

I think because it's only uncommon, and there is no immunity to mind attacks, I'd say that if your intelligence is dropped below 19,the band stops working 

Except that's not how it works.   (As far as RAW is concerned, I can't speak to how anyone deviates from RAW)

If you're wearing a magical item that sets an ability score to a specific value and are subjected to an ability score reduction your original score is reduced but the magical item still keeps it's value. 

Now, if the Intellect Devourer reduced your score to 0 AND somehow manged to knock the headband off of you then your Int would drop to zero.   Otherwise your score remains 19 until the headband is removed. 

Crawford has weighed in on this already as well: 

https://twitter.com/JeremyECrawford/status/846382901147004929

Sorry, this makes no sense.   I get where Crawford, being leery of making a change to the rules after publication, would say that the effect of this relatively minor magical item would keep the stat at a certain level, but I am telling you rulings like this make so logical sense.  Ability damage should reduce the score of the character, regardless of magical doohicky,  and the effects of that loss should be felt by the character until a restoration spell is cast.   This kind of immunity to ability drains is not listed on the script by the item, and because it is not listed as a quality we should not be reading into it.   Of course, you guys are free to run your tables the way you want and to use unofficial (read: non Errata) rulings to guide you.

I don't see it as really reading in to anything.   

The Headband of Intellect says:

"Your Intelligence score is 19 while you wear this headband."   (Caveat, this is based on the DDB entry, I don't have my hardcover handy to look it up to see if there is a different wording)

It doesn't say it increases your score by a number, or to a number.  It just IS 19.  The item doesn't care if you had a 1 in Int or 18 before putting it on.  The only thing it cares about is if your Int is less than 19, and if it is then it's now 19.   

I don't think it's fair to call it a "relatively minor" magical item either.  Sure, it's only uncommon, but it also requires 1 of your 3 attunement slots.

Also, it doesn't prevent the ability reduction.  It just doesn't care what that score is while being worn. I could see an argument being made that IF the reduction takes your actual Int to zero the stun effect is still in place and requires restoration. (I wouldn't rule it that way personally though. )

 The intellect Devourer's Devour intellect only can take up to 3d6. If the attack targets the current int from the headband, it wouldn't work, because 3d6 can at most roll a 18. If it targets the base int, then it has a chance of dropping the base int to 0, but the target would remain with 19 int, because the headband keeps it there

Certain magic items offer  protection from rare attack forms.   You can't:

• use Magic Missile against someone with a Brooch of Shielding
• target Mind Spike against someone wearing an Amulet of Proof against Detection and Location
• effectively use Feeblemind or Devour Intellect against someone wearing a Headband of Intellect.

Nothing unusual at all.  It simply does not work.

First off, it's not damage on the INT score, it's changing the INT score to 0 from specific criteria.

From the Headband of Intellect entry:

"Your Intelligence score is 19 while you wear this headband." Basic Rules. p.173

Re: Intellect Devourer (MM p.191)
From the "Devour Intellect" ability:

"Also on a failure, roll 3d6: If the total equals or exceeds the target’s Intelligence score, that score is reduced to 0. The target is stunned until it regains at least one point of Intelligence."

3d6 can never beat 19 as Margaret22 pointed out.

Devour Intellect does not mention any brain consumption. As far as RAW is concerned, it's only devouring "intellect" and not the actual brain until it uses its "Body Thief" ability on an incapacitated target. Since regaining 1 INT removes the Stun condition, the brain has not been consumed with Devour Intellect. Body Thief requires the brain to be returned by some method such as Wish.

From the Body Thief ability:

"The intellect devourer is also forced out if the target regains its devoured brain by means of a wish. By spending 5 feet of its movement, the intellect devourer can voluntarily leave the body, teleporting to the nearest unoccupied space within 5 feet of it. The body then dies, unless its brain is restored within 1 round."

I would be forced to rule that the headband grants immunity against the INT=0 on a failed save from Devour Intellect, but of course, the target would still take psychic damage on the failed save.

EDIT: The headband does NOT prevent Body Thief if the target is incapacitated.

"Body thief: The intellect devourer initiates an Intelligence contest with an incapacitated humanoid within 5 feet of it. If it wins the contest, the intellect devourer magically consumes the target’s brain, teleports into the target’s skull, and takes control of the target’s body."

I don't understand what interpretation that is.

The headband sets the score to 19. The Devour Intellect failed save only roles rolls 3 through 18. The Devour Intellect says nothing about challenging the natural Intelligence score. By that, RAW accepts a magical score of 19 as the value to beat regardless of the natural score which Devour Intellect on a failed save cannot do.

Unless your interpretation adds the word "natural" to the phrase "intelligence score" - a word that's not there in RAW, the headband's intelligence score applies instead against the 3d6.

EDIT: rolls, not roles *facepalm*

I agree with EricHVela on this one; the Intellect Devourer can't reduce your Intelligence with this ability while the headband is equipped, and even if it could it can never trigger that condition anyway, so I'm not sure of the issue here.

There isn't really a precedent in the game that I'm aware of for distinguishing between a natural ability score and a granted one; while wearing the headband your Intelligence is 19 and that's that, your normal score is irrelevant until the headband is removed (or your normal score becomes 20 or higher somehow). 99.999% of the time, whatever your normal score might be doesn't matter, all that matters is your current score, which is what the headband changes.

Loads of magical items make you extra strong against specific enemies, but they're still only uncommon because the vast majority of enemies can and will still hurt you. An Intellect Devourer can still hurt you in fact, it just can't incapacitate you this way, but if you're incapacitate by some other means it can absolutely try to eat your brain as normal. This is really an argument for why a DM should avoid throwing groups of identical enemies at players, as it's usually good to have two or three types so that the group, or individual players, can still be threatened by some of the enemies to maintain the challenge.

Time stamp between posts #6 & #7.

Patches asked a new question related to the subject and had new insight into the subject, and it's a question on which reasonable interpretation can differ, and it provoked new thoughtful analysis from other posters. Relax. 

I, too, subscribe to the "life support" approach, where stat damage is done to the base stat, but doesn't effect their effective total so long as they remain wearing the item. But if its taken off, they'd drop to 0 and suffer... a bad time.