When shift clicking inventory items in your 'backpack', and they have nowhere to go (ie, to a chest/furnace inventory, or in the case that particular armor slot is occupied), instead of doing nothing, the item just vanishes - very similar to the creative mode delete box.
Shift clicking when in the "E" inventory screen just flat out deletes them.
Same issue replicated on a horse.
unconfirmed: mule with inventory
Related issues
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duplicates MC-88929