You are right about the repair bot quest, but I did have the damage patrol bot pop up. Hence, the question.
So, where does the damaged bot go? If I remember correctly when I got the quest, it did say something about better to have support for the bot. However, I did not recieve the damaged bot for repair. There's also no request for replacement. I was just a bit confused there.
The game code is structured such that all bots in the game belong to the player and are located either at "Home" which means in a capsule or in their "Workshop" which means in storage. This means there is no "location" to put a bot when you do not have an empty capsule or free space in storage. (The only exception is in the new "Business Partners" quest but to avoid a spoiler I won't say anything more about it.)
When you give a bot to the patrol it is removed from the game because it cannot be in a capsule or in storage and there is no other place to put it. When you receive a damaged patrol bot it is never the one you gave to the patrol, it is a new bot created for the purpose. When this bot is created a "Task" is created which you can view in the "Journal" telling you there is a patrol bot you need to repair.
If you receive a damaged patrol bot when you have no available space two flags are set in code but the bot is not actually created. The first flag is to remember that you received a damaged bot and the second flag is to remember if it's male or female. Unfortunately, since the bot was not created there is no "Task" added to the "Journal" yet and there is no way for the player to know about this except to remember that it happened. I'll put adding some sort of reminder on my "TO DO" list but until this gets done you just have to remember there is a "damaged bot waiting for space".
Throughout the entire game each time a turn ends a function is run that checks to see if these flags are set, i.e. you have a damaged bot waiting for space. If the flag is set it looks for an empty capsule. If there is one it creates the bot and puts it in the capsule. If there is no empty capsule it checks for available space in storage. If there is space available it creates the bot and puts it in storage. If the bot is created then the "Task" is added to the "Journal".
There can only be one bot "waiting for space". I did this to simplify the situation for myself. In principle I should have made the "flag" a "counter" and allowed the total number of damaged bots in capsules, storage, and "waiting" to be equal to the number of bots given to the patrol. This is 0 when the game starts but increases to 2, then 4, and then 6 as the player completes the Good Neighbor quest. Perhaps one day I will change the "flag" to a "counter" but I'll put it on my "MAYBE SOMEDAY" list instead of my "TO DO" list.
