Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your fellow was hit by a car a week ago, suffering tail trauma with swelling and has now bitten the bottom half of his tail off.
I suspect that what has occurred is a result of a tail pull injury or tailhead trauma.
This occurs when a pup falls and lands on his tailhead/back of the pelvis or the tail gets caught (by another animal or a car) and pulled hard enough that the caudal spinal cord is stretched. Sometimes the nerves are just stretched, but in some cases they break and when that happens the damage can be permanent. Dogs may not show the full extent of their injury for several days as secondary inflammation and nerve death occur.
As the nerves try to reconnect there can be a tingling sensation, and since feeling in the tail isn't normal when the pup bites/licks at the tingling area they cannot feel the damage they are doing and can actually cause significant trauma, as you pup has.
The other possible causes of his chewing his tail are an intervertebral disc protrusion putting pressure on his spinal cord, or a blood clot within the spinal cord canal which is placing pressure on his spinal cord and causing a tingling sensation.
If he is having trouble passing urine or stool he should be seen by a veterinarian as soon as possible. But if he is able to eliminate normally I recommend that he be closely confined tonight, have an elizabethan collar placed so he cannot further traumatize his tail, and then see his veterinarian tomorrow morning.
They can examine him and will likely need to surgically debride the area he has traumatized and close it surgically and prescribe antibiotics to prevent infection.
If he is also getting weak or uncoordinated in his rear, or having trouble passing urine or stool, then we need to worry about more serious damage, either to his spinal cord, or lumbosacral joint or spinal nerves and then you may want to discuss further testing with your veterinarian as well as referral to a veterinary neurologist for an MRI.
Best of luck with your fellow, please let me know if you have any further questions.