Animals that are the least specialized generally stand the best chance of survival when the environment suddenly and drastically changes because they are able to -

The answer is Because they are able to adapt to different conditions.

The least specialized animals are those animals that can survive in a wide range of different environmental factors, unlike specialized animals which are very sensitive to changes. If environment changes suddenly and drastically, highly-specialized animals could not survive because those changes are beyond a range of different factors that affects them. The least specialized animals could adapt to different conditions. For example, one species (specialized) lives in a temperature of 20-25°C. The other species (the least specialized) lives in a range of temperature 5-50°C.
If temperature changes drastically from 22°C to 10°C, the specialized species could not survive and the least specialized would just adapt to those conditions.