Is it possible that an epidural steroid injection can go not deep enough and instead inject the subdural space?

Technically no.: The epidural space is closer to the skin so, if you do not go deep enough, you will be outside of the spinal canal. The subdural space is deeper to the skin, so by not going deeper, you will not go into the subdural space. What can happen, however, is the needle does go too deep into the subdural space causing potential nerve irritation, and injection of steroids into the spinal sac.

Anatomy: If the epidural injection doesn't go far enough, it will not enter the subdural space.

Actually...: Yes that can happen, however use of X-ray equipment during the injection makes that less likely. Also the subdural space is going too deep and your injection would be in the spinal fluid area. this is different than you suggested in your question. While this is a possible place to put the medication, the likelihood of irritation to the nerve roots and spinal cord is higher.