If your inventory is full, and you have a stash, pick up an item (if your stash is not full), it will be sent to the stash. This would be a great suggestion (imo) because most people don't like it when they pick up a red box, it says your inventory is full. If you have a stash.. well it would be sent there! Well of course, only when it's not full.
"Items cannot be sent to your stash/inventory because it is full."
"Items cannot be sent to your stash/inventory because your inventory is full and you do not have a stash."
It would also say what you got.
"Items cannot be sent to your stash/inventory because it is full. The item you got was -----."
"Items cannot be sent to your stash/inventory because your inventory is full and you do not have a stash. The item you got was -----."