Aside from those weird on-call cases (engaged to wait/wait to be engaged), you are legally required to be paid for work that you do.
You cannot and should not accept being “off the clock” for a single thing the employer requires of you.
If you call in sick and your boss requires you to call around to find a replacement, CHARGE THOSE FUCKERS FOR THE TIME YOU DID THEIR JOB. If you have to prepare something for your job before you can start doing a main duty, CHARGE THEM FOR THE TIME YOU DID THEIR JOB.
If they don't pay you, there are paths to fight them for what you are owed. Stop letting employers screw you out of the time you provided work to them.