Description revised as of 0.15.90.2 rplatham:
When picking up items, the game does not seem to check to see if the stack should be split so that some of it stays on the ground because picking up all of it would overfill the player's inventory.

Example to Reproduce

1. Fill all slots of your inventory and include two stacks of the same item (for this example, we'll use two full stacks (64) of coal)
2. Place some more coal (say 16) in a chest nearby.
3. Drop one full stack of coal from your inventory on the ground.
4. Go get the 16 coal from the chest.
5. Now pick up the full stack of coal from the ground.
6. Observe that you now have two full stacks of coal in your inventory and there is no coal on the ground.

I expected that the full stack of coal on the ground would become a stack of 16 coal on the ground since your inventory could only hold 48 more coal.

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Old Description

• Add a full stack of some items to a chest
• Add a non-full stack of the same item to your inventory
• Fill all other slots of your inventory with anything else
• Open the chest (Screenshot 1)
• Long-click the item stack in the chest and transfer all of it to your inventory (Screenshot 2)

It works and nothing remains in the chest.
A stack of the remaining items is now stored in an invisible slot of your inventory. (Screenshot 3)

It isn't accessible directly, but if you try to send more items of the same type to your inventory from a chest they will stack on it (Visually they disappear but in fact they stack there, the problem doesn't happens when you send the item from a crafting table output, only from a chest)

If the item type is a combustible or something that can be burnt, the "invisible" stack is still available in the furnace UI.

It's not the only case where it happens but it's the easiest to reproduce.
In the screens I managed to make all the wood disappear from my inventory but that wasn't voluntary and I don't know exactly how, the inventory is sometimes a little strange when there are some invisible stacks around... (Screenshot 4)

Other way to reproduce by kaleb418:

1. Fill inventory up with random items.
2. Say, for instance, you have a stack of coal in your inventory. Throw out the stack of coal onto the ground.
3. Get another stack of coal in your inventory. Place down a chest. Make sure your inventory is still full, with one stack of coal in your inventory and one stack on the ground.
4. Change game mode to survival.
5. Put some coal in the chest, but still keep some in your inventory so there are no empty slots.
6. Pick up the coal on the ground. It will all go into your inventory, and the remainder of the coal that doesn't go into the visible slot will seemingly disappear.

Update by nighter
This bug has been reported to our internal bug tracker for further testing and a fix. It is scheduled to be fixed in one of the future updates (no specific date can be provided).
Please avoid duplicate comments. Post only NEW information regarding this bug.