Depends on the plastic, but even the most benign ones put out very minor amounts of fumes if YouTube testers are to be believed. Note that fumes in this case just means that they are seeing changes in AQI meters, which is something that can happen with too many people sitting in a room.

If it’s something you worry about, the enclosed models frequently either come with, or can be fitted with a carbon filter, and if you are really worried, you can use dryer vent to get it outside.

With the most popular plastic (PLA) at printing temperatures, there isn’t any data showing toxic byproducts. When you get into things like ABS and resin you have to think more about fumes.