Tameable pets with collars dropping their collars upon death

Everyone knows how animals like wolves/dogs and cats have collars upon being tamed that can be dyed. I believe that these animals should be able to drop their collars upon death, eg if the dog was named willow for example, "willow's collar". This would be sad but it could be used for shrines and memorials for our dead Minecraft pets and overall it would be a pretty interesting detail.