Do a quick search and you can find the properties.
I have stuff 50 years old, like Mike, one batch brittle (For example WW2 Airfix Germans 1st type )and some as perfect as the day they came from the box.
Daylight, sunlight heat, dessication etc may have a very slight effect but the fault is likely to be in the manufacture- wrong temperature, wrong pressure or wrong recipe or a bit of all 3. Brittle -ductile transition in polyethylene effected by cooling time is probably the cause. Basically it develops a crystalline structure. Impact properties are adversely affected by aging, annealing, and adding other thermoplastics. Older polyethylene doesn't have the same springiness as new but that is not a great problem with figures but the issue of developing a crystalline structure or brittleness does because they fall apart to the touch.
How can you tell and save a precious collection?
Firstly they are not precious they are mass produced plastic so if you paid a lot for an old set and they fall apart it might make you think again.
Usually the crystalline transition results in a lack of oiliness and the figures seem to dry out but this can be over a period of years. Impossible to detect if the figures have been coated with paint,varnish etc.
Don't buy big batches which is why so called limited editions are annoying. You can end up with lots of crumblies.
If they have gone crumbly as Mike says throw them out or enjoy scrunching them up and then throw them out with an incantation like - ....ing plastic figures
Most don't crumble or go brittle. Correction most don't crumble or go brittle before we do. Entropy.