Could a bad steering box or one that is going bad cause different types of steering pump failures?

 

typically no, unless there's serious leaks. but i'm curious, define "different types" of pump failures.

 

They were rebuilds(2 of them).I just put on my third one, but this time with a new steering box. Mine(steering box) had what they call morning sickness. When I first get in the truck the power steering was a little intermittent for 5 minutes and then goes away.The fluid was black and had a burnt smell. The first pump started whining after the first week. The second pumps shaft broke in half inside the pump after three weeks while making a sharp turn into my driveway. Now it steers great, but I hope it lasts. Is it cheap rebuilds or was it the box? I see your from KY. I have a LOT of family there.