I don't think all therapists schedule the same; some give the client a set time each week (mine) and if you don't appear you pay for the missed session and some make an appointment one at a time or have the client call the office to make an appointment through their secretary. If you call and cancel that appointment, it's gone, you go to the end of the list and make a new one. Sounds like in this instance he made an exception and kept a slot open all the time, so none of his other clients could ask for and find that time slot open. However, it sounds like he did that on his own (without discussion with her) and she was in the habit of coming/not coming and was not part of any "contract" with him since he'd decided to try this on his own as part of how he was treating her.

T's usually tell you straight out how they "work" and how your sessions will be arranged. I don't know how yours feels about late you come/don't come and if an emergency came up, would they put someone in your slot if you weren't there, etc. I learned to call my T to let her know when I was going to be more than a few minutes late; so she wouldn't have to wonder and would have a clue when I'd show up. If I was late, does not matter what the cause, we only went to our normal end time; if she was late (arriving), she'd get word to me and she'd go over so we had the whole session. Start late because of her fault, I get my money's worth; start late because of my poor planning/fault, I get my session minus the late time.