I was messing around with command blocks and made one that repeatedly summoned items with the elytra in one of it's armor slots. When you have a full inventory and are not supposed to be able to pick up any more items, it will still pick up these items. The items do not show up in your inventory and are thus deleted.

Command I used:
/summon Item ~ ~10 ~ {ArmorItems:[{},{},

,{}]}

Steps to recreate:
1. Generate a new amplified world in creative mode. All other settings are default.
2. Fill your inventory with any kind of block / use a command block, set on repeat, to fill your inventory with the blocks.
3. Open the creative inventory and get a stack of items by shift-clicking, and drag them out of the inventory to drop them.
4. Pick the items up.
5. The items should not be in your inventory and will be gone.