A family friend once told me that on elk, the best thing you can do is crowd the shoulder on your shot- if you hit just behind, you get the vitals, if you hit the shoulder the elk might not die right away but it won't be able to go anywhere and you can put another round in the boiler room to finish the job.
If you break both shoulders,an elk is immobilized,if you break only one,an elkcan run faster on three legs than a hunter can run.And they can run for a long time with one broken shoulder.I have on occaision fired a follow up shot on elk or moose,as they can be difficult to recover if they reach cover,but usually the animal is on the ground before I even get the chance.