Escaping a city is an optional action that may happen at the very end of your turn. It has no dependency on any previous action during your turn or scoring (you may have placed a meeple or not, or you may have removed and scored an abbot, or completed and scored another feature, or maybe performed any other action taking place during a normal turn).
The idea is that you may remove a knight placed in a besieged city and return it to your supply without scoring anything. How can this be useful? Well, it allows you to recover an idle meeple that may be trapped in that city or won't be able to reach the majority.
So addressing your comments...
The rules are clear that you can’t escape a follower from a besieged city and then place that same follower back on the board. The escape happens and the very end of your turn.
Correct.
The rules are not clear about placing one of your followers onto the tile you just played, then in the same turn, escape one of your followers from a besieged city, through an adjacent Monastery.
The meeple placement may happen as usual on the tile just placed. At the end of your turn you have this additional option to remove one of your meeples meeple from any of the uncompleted besieged cities on the board.
Can you place and then escape in the same turn?
Yes, escaping is an action not influenced by any previous action during your turn.
Modified for clarification:
This question is being asked because of the rules for the Abbot. The rules clearly say that:
“On your turn, if you do not place a meeple during the 2. Placing a meeple phase, you may instead return your already-placed abbot to your supply. If you do so, you score immediately as many points as the garden or monastery your abbot occupied is worth at that time”
The rules for the besieged cities seem to indicate that you can remove your follower even if you did place a meeple, and, even if the rules did not say it, I assume that the escaping follower does NOT score any points!
Correct. You recover one meeple and score no points for it. It has nothing to do with the abbot.
- You may remove and score an abbot as an alternative to placing a meeple (This is a special type of scoring).
- You may remove a meeple in a besieged city at the end of your turn via a monastery adjacent to the Besiegers tile (This is a way to recover idle meeples from a city)
Let me know if you need any further clarification.
Note: If you are interested in expansions allowing you to remove meeples, please also check The Festival:
https://wikicarpedia.com/index.php/The_Festival