I live near CSX Avon Yard which is a large hump yard on the main route between Cleveland and St. Louis. I made the mistake of putting the HOT frequency in a scanner. For the most part, all I heard were HOTs since there are so many locomotives around the yard. I locked out the HOT frequency, but I've left the EOT frequency in the scan list. It's not much of a problem unless I'm on the periphery of the yard.
In my experience watching trains at Avon Yard, the car inspectors grab the EOT off of inbound trains as they inspect the trains in the receiving yard. They may switch off the EOTs at that point. The EOTs travel in the back of a car inspector's pick up truck to a small shop near the departure yard where they are serviced and tested. After that, the EOTs hang on a rack outside the shop. The car inspectors then hang the EOTs onto outbound trains in the departure yard.