If you spend enough time climbing with me, you'll find I do a surprising amount of things that I will go to great lengths to make sure you don't do.
Daisy chains have been a staple of aid and even trad climbing for decades. They are very versatile but have major drawbacks. This is why you should avoid using them as Personal Anchor System as much as possible. Dyneema or Dynex daisy chains use bar tacs to create pockets. They also are what's known as static, meaning they don't stretch. Combined, this means that in the event of a shock load (i.e. you fall on the chain) the pockets could explode, referred to as "pocket failure".
Now, the average daisy is rated around 20Kn of force. This, however, is the rating for the chain as a whole, not the individual loops. CAMP has attempted to compensate for this issue by creating the "daisy twist" which reduces the chance of pocket failure by wrapping and doubling the stitching for each loop. A good strategy but probably not perfect.
While it is unlikely a fall that is less than a class 2 would generate enough force to completely destroy your daisy, once even one bar tack is broken, the material is compromised.