According to the "piggy bank bug" excerpt on the Terraria Wikia page of Known Bugs,
Sometimes items in your inventory will be removed, but only small portions of them. This is a sign of a save that is soon to be corrupted
It appears the bug corrupts the ID number of the item in the piggy bank. I could speculate that the item ID and stack count are being calculated together, as you could exploit the bug to deliberately create glitched items. It appears the "random item" generated is actually determined by the item ID and stack count of the original item. For example, a stack of 3 dirt would generate stone.
The problem with this is that it can corrupt your save.
Once your save is corrupted, it can be difficult to fix. The standard fix for corruption is "wipe and restart". Is the game crashing on launch, or does it only crash when you load the world? If just the world is causing the crash, at least you only have to bomb the world, and not your character.
You will notice that the bug is now listed as a fixed bug, so updating your game over Xbox live should guarantee this does not happen again. Better yet, you might find that updating the game fixes your problem from the get go.