“Would you be willing to write a recommendation?”
He’s asking the person who managed his termination for a recommendation. Because the world he’s entering requires references, and the only people who can speak to his work are the people who decided his work wasn’t worth keeping.
The recommendation letter is the final performance. The institution performs generosity — “he was a valued member of the team” — and the person performs gratitude — “thank you for your support of my career.”
Both know it’s fiction. Neither says so. The recommendation letter is the last thing the institution gives you, and it costs them nothing, and it says nothing, and you need it desperately.