I just read that they can release hydrofluoric acid (HF) and other toxic chemicals under conditions of chemical leakages, overcharging, external heating, or explosions.
Now, hydrofluoric acid (HF) in particular is extremely toxic, whether inhaled, touched, or ingested. An explosion can also cause a fire.
How concerned should we be about this release occurring in common household electronics like phones, laptops, and battery packs?
Is the risk greater for old, depleted, or swollen batteries? Are LiFePO4 batteries safer?
What tips can help keep one safe?
How big an "event" occurs when a battery is damaged to the point of self-immolation is correlated with its level of charge. A fully-depleted battery won't do much if damaged. A fully charged battery will vary from "it gets really hot" to "boom," depending on how it is constructed. Thus, if you have a LiIon battery that you want to dispose of, it's always better to safely discharge it as low as it will go before storing or transporting it.
Lithium-polymer ("pouch") cells are cheap to make and are incredibly energy-dense compared cylindrical cells (such as the classic 18650), but are far more likely to go kaboom. Unfortunately, they make up the majority of our Lithium-powered gadgets.
LiFePo4 cells are MUCH more stable than either traditional lithium style, handle over-charging better, and survive far more charge/discharge cycles. The tradeoffs are that they are a bit more expensive and are slightly less energy-dense. I have also never seen them in "pouch" form, so I don't know if they can ever replace lithium-polymer for cell phones/tablets. But they are pretty popular now in power tools and car/bike batteries.