"Systematic reviews of controlled clinical studies of treatments used by chiropractors have found no evidence that chiropractic manipulation is effective, with the possible exception of treatment for back pain.[8] A 2011 critical evaluation of 45 systematic reviews concluded that the data included in the study "fail[ed] to demonstrate convincingly that spinal manipulation is an effective intervention for any condition."[10] Spinal manipulation may be cost-effective for sub-acute or chronic low back pain, but the results for acute low back pain were insufficient.[11] No compelling evidence exists to indicate that maintenance chiropractic care adequately prevents symptoms or diseases.[12]"
All the time? No, but it's happened before. Particularly with high neck manipulations that sever the spinal cord above the point where the nerves that control autonomic functions branch off from the neck (I think that's C2?) Randomly? Also no. It's a very predictable result of spinal manipulation. Just like lung cancer doesn't happen 'randomly'; if you smoke enough and long enough, it's pretty likely, but if you don't smoke at all it's very, very rare.
It's definitely happened. I think the technical term is "vertebral artery dissection." I don't think it's like a daily occurrence or anything, but there is a very real risk of it happening whenever you get a chiropractic adjustment on your neck. Basically you have some delicate arteries running through your neck bones and the sharp sudden movement of certain chiropractic adjustments have the potential to rupture them. It can cause a stroke and some various other bad things that can happen when blood flow through the spine is interrupted.