Normally this is caused by the fractured vertebra crushing the front of the spinal cord. The nerve pathways at the front of the spinal cord are damaged resulting in these patients being fully paralysed with the loss of hot and cold or pain sensation.
The pathways at the back remain undamaged. These pathways transmit sensation from the body to the brain regarding light touch to the skin, vibration sense and the ability to know the position your joints are in without needing to look at them i.e. elbow straight or bent.