Anyone ever seen or heard of something like this?
Sure, it happens when you get the power supply connections wrong on a PCB design for instance.
Its good practice to connect a 'new' design up for the first time with a current limited power supply, this way you can identify problems before they get a chance to fry something.
Unplug the XBee.
Measure the current comming out of the battery, how much is it, is the current level normal ?
Plug in the XBee.
Measure the current comming out of the battery, how much is it now ?