I believe you are confusing your terms. An oil rig is the infrastructure used to drill the well. Here's a picture:
Once the well is finished, the rig is moved to the next site.
A key number in the oil industry is percentage of rigs in use. During boom times, the percentage would be near 100%. If a rig is not in use, someone is losing money.
Producing wells have operating costs. At $30 per barrel, some wells become uneconomical and will be shut down. In most instances, a well that is shut down will not be restarted.
I live near some of the past best oil land in the world. Many fortunes were made....
Now...very little drilling at all.
Just stripper wells around here now...
Some guy's a few years ago...were drilling for what the geo guy's said was big pockets of Helium..They wore out numerous bit's...and ran out of $$$..and stopped the operation.
Everything you said...was spot on. And I'm not in the biz.........