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This is an easier and more accessible version of the item underflow glitch (https://www.youtube.com/watch?v=w4Yr2Nz4rFU) that does not require a drink (and the Saffron guard being thirsty) or a Fossil. I think it may have been found by luckytyphlosion, I'm not sure.

Item underflow lets you access items beyond slot 20, which represent unrelated memory addresses, allowing you to change a limited number of variables in the game by tossing those items or replacing items found there.

It involves a stack of 255 items. You can get one through various methods: http://pastebin.com/DfwS1Qbn

Tossing an item above the stack of 255 items (or a stack of 255 items itself when it is at the top of the items list) lowers the number of items in the pack but does not affect the rest of the player's items.

Before dry underflow, previously you had to lower your item count to 0 by continuously tossing an item x255 at the top of the items list. Then you had to trigger an event that takes an item from your inventory (i.e. Saffron guard taking a Fresh Water or the Cinnabar scientist taking a Fossil) to get 255 items (the result of the game doing 0-1). This old version was found by MrWint.

Now you only require two items and a stack of 255 items.

Dry underflow steps (thanks luckytyphlosion):
1) Order your items so that your 2 tossable items are in slots 1 and 2 and the item x255 is in slot 3.
2) Toss everything below the item x255.
3) Toss the top two items so you have three items x255 (item count=1)
4) Toss 253 of the first item x255.
5) Swap item 1 with item 2.
6) Swap item 1 with item 2, again.

Do this all in one go. If your number of items becomes 0 (after step 5) then you can mess up if you back out of the menu before finishing as you wouldn't be able to swap the first item with the second.

You can also do this with items below the third (and initial) 255 stack. You need to count how many items you have, then after step 3 toss the top item x255 the number of items you initially had -2.

A cool thing about dry item underflow is that it works for the PC storage box. This allows for manipulation previously only possible through arbitrary code execution and map FE (https://www.youtube.com/watch?v=mUQxe0GqPBY).

Surprise: I decided to show off D5F0 (stored PC item 92) corruption in Pokémon Yellow, an address that controls events in Pallet Town. I set it to 35h (Revive), and this corrupts the Pallet Town music by making the game play the in-battle sound bank, theoretically forever until you change it again!

More information about dry underflow:
http://forums.glitchcity.info/index.php/topic,7175.0.html

Dry underflow has already been used for speedrunning. https://www.youtube.com/watch?v=pvY1QJ5uSPs