Brass instruments (not just the trombone) can have micro-adjustments in pitch through the embouchure (lip position/tension) of the musician.
(1) Example: "get up an get out" by Iggy Pop. https://www.youtube.com/watch?v=R1ld5jG3f-M
usually that’s not the case though. typically it’s individual notes. much harder to precisely and accurately modulate tape velocity (especially by hand).
So basically, a woodwind like a sax will tune a few notes with a piano or whatever, but it's really up to the player to keep playing in tune. I would not even bother trying to autotune or use post-processing; it'll just sound weird.
This is also how you can get a room full of student musicians "tuned" but it still sounds like a disaster.
This sort of hybrid tuning is common in barbershop quartet singing as well.