Fire risk with Li Ion batteries is while charging and when they are short circuited which can be caused by several things.It only needs one cell out of many to ignite and set off a chain reaction in the rest of the cells, a la the 787 battery debacle.
The 787 batteries and charger weren't 'cheap',so it can happen to any battery with this chemistry,especially large capacity types.
I never leave my laptop powered up overnight on my desk,and never charge any large capacity Li Ion batteries without supervision and well away from anything flammable.Small ones in mobile phones don't seem to have issues,but there may be cases out there which I'm not aware of.
Li Ion batteries will go bang while in storage too. I had one for a high end EBIRP to that in my office in Singapore, a brand new one at that.
The smell stuck for months and the soot had to be painted over.
Scary stuff.
Per