Bearded dragons are unable to drop their tails for any reason. Though many species of lizard naturally have this ability as a way to evade predators, bearded dragons are not one of these. They can no more drop their tails than a cat or dog 
Lizards who can naturally drop their tails have built in mechanisms that seal blood vessels so little to no blood lose occurs when they drop their tails. Iguanas do have a slightly different method as their tails can break at certain points along the entire lengths but again, these methods are designed to happen with little to no blood lose or trauma. Also, not all lizards who can drop their tails can grow them back. Crested geckos are one such lizard I am aware of, they can drop their tails, in this case the entire tail, but they do not grow one back. Instead the tiny bit of tail seals over and becomes more like a knub. The loss of the tail doesn't impact on the gecko's life at all. Other species of lizards and geckos will grow their tails back after dropping but the regrown tail is never as long or patterned as the original was.
Typical bearded dragon tail injuries are the result of cage mates nipping the tail tips thinking it is food. This usually happens with hatchling and young dragons kept together in a tank and not fed often enough or just having too many in the cage. Even older dragons can bite off tail tips or toes if cage mates do not get along.
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