Yup. Been there and done that.
For the most part, when these were installed, they were hung in the hole then concrete was poured into the bottom of the hole.
This would flow under the end of the cylinder and fill the bottom 1-2 feet of the hole. Back filled with dirt up to around 4-8 inches of the top, more 'crete at the top, done.
The fun part of removal is getting the darn thing to at least wiggle in the hole so it can start to be lifted.
I hand dug approx 1/3 of the way down along the cylinder then I had a friend of mine use his backhoe and he simply started pulling back and forth while lifting. It took a bit of this but it finally came out of the ground.
After removal is when the "Rock of Gibraltar" was discovered attached to the end of the cylinder casing. Then talking to a couple of guys 'in the know' after the fact is when I found out about the way these were most commonly installed.
When I installed it in my garage a 4'x4' area was cut into the floor. Then the hole was dug approx. 1 foot deeper than the casing length.
At the end of the casing there's an approx 1" lip on the outside edge. I found a piece of pipe that would fit inside the lip and placed it into the bottom of the hole, poured cement into the bottom to the correct depth (length of casing) and let it harden. Sat the cylinder onto the slab, leveled it, back filled, and 6" of 'crete to floor level.
This was back in '86 and I don't regret my decision of getting the 'free' hoist.
BTW, the one I got has a separate tank and the cylinder/casing don't weigh a whole lot. I installed it using a chain fall suspended from 4 roof trusses bridged by a 2" schedule 80 pipe.
It also didn't have the top with the arms installed on top. That was removed before removal and put on after it was in the ground
Hope this helps and is reasonably easy to understand.