"Puffed" batteries are both more and less dangerous. I am drawing from over 10,000 FPV flights where I beat the mortal sh*t out of lipos and also from over 3000 battery charges I have logged and analyzed (I built an app for that).
I read the other comment and that person knows their chemistry. I will try to balance that information with real world experience.
Decreased danger is minimal as a puffed battery will not hold nearly as much charge as a good battery. I have nailed, cut, crushed, and set on fire all states of battery and puffed ones never make me go "wow", they hold less energy.
However, puffed batteries pose several true threats.
One danger is how the "puff" adds stress on the foil wrapper and crimp used to keep the juicy bits inside. So a puffed battery is much more likely to puncture in travel, general handling, use, or charging -- it is stressed. The internal "juice" is pretty toxic and that is reason enough to move on.
As a puffed battery will hold less energy don't count on the performance being the same. Sag is real, and as a commercial FPV pilot I am counting on the punch I need to get where I want to be. Anything less is a danger to my gear and those around. We fly mostly chase scenes with large vehicles, any failure is quite serious.
Another consequence of bad or old batteries is voltage swing. If you black box or watch live voltage data on a puffed 4s (16.8v charged) you will see the voltage immediately drop to sub 8v on first punch. That is too low, even for a second. A good (100c+) 4s will never dip much below 12v on the same punch. Sudden low voltage can upset the electronics and balance. I have burnt up a number of VTX recently by dropping voltage too low.
Even though puffed batteries produce less "wow", they still are dangerous and could ignite other batteries, so separate them (I carry 2 lip bags usually).
A lipo is only good until it is not. As soon as it is not safe to fly assess the condition and take action immediately. If not dead, but too lame to fly normal and safe I keep as a "scout battery" or "desk battery". A scout battery is my first battery to use where I simply hover and make sure all radio gear is good and see if any EM problems exist before full flight. Desk batteries I use for testing builds and buffering power supply. So many batteries may go weak but still be safe for limited or testing use. If you are not familiar with battery life cycles and detection of flaws please dump them correctly and immediately.
Finally - I have had a person close to me loose the entire house by charging LiPo batteries unattended. The threat is real and if this happens expect the insurance company to try and not pay claiming you "did not follow the instructions for safe use" and deny a claim. That is what happened to our friend. So being cheap on battery tech can cost you everything, I have seen it first hand.