Only when the last item is removed is there risk of destroying the box or egg. This is almost a convenience with common boxes and eggs, but can be considered a disaster when dealing with GM Gift Boxes or GM Eggs.
The method detailed below seems to consistently prevent the destruction of a box or egg when removing the last item. Be sure to practice first to verify that this method is currently working.
To remove last item without destroying Gift Boxes and Eggs:
1. Put the Box or Egg into your inventory.
2. "Look in" a backpack in your inventory.
3. "Look in" the Box or Egg.
4. Click-and-drag item(s) from Box or Egg to the backpack.
Do not release mouse button until item is dragged to backpack.
WARNING: Buy some eggs or gift boxes, put 1 gold in each, and practice before attempting on valuable items.
If the above is followed exactly Box or Egg will not be destroyed when last item is removed. Always test first with non-valuables.
A pouch, or another Box or Egg may be substituted if you don't have a backpack, but note that the same problem will exist when it's time to get the last item out of any Box or Egg.
Step #2 may be skipped if the item is dragged onto a container in your inventory, and released with the "put-in" icon visible.
The Box or Egg will be destroyed if the item is dragged into inventory (instead of a backpack or other container in inventory).
The Box or Egg will be destroyed if the "take" button is used, or if the item is dragged on itself and released to remove it.
The Box or Egg will be destroyed if Box or Egg is on floor.