How do I fix a left thumbstick that has gone completely loose?

If your Xbox One Wireless Controller has a malfunctioning thumbstick and you cannot properly navigate around your Xbox One, see the Xbox One Wireless Controller Has Malfunctioning Thumbsticks problem page for possible problems and solutions.

sounds like the arm for the analog control has snapped there are two ways to fix this problem open your controller and depending on how close to the analog unit it has snapped you may be able to glue it back on making sure to remove the broken piece from the analog stick first (this will make it easier to align/position ) and not get any glue on the two skinny arms that run horizontally which control the left and right movement of the analog also use an epoxy glue like Araldite DON'T use super glue as it will break very quickly.

The other way is to replace the analog and order part from eBay for around $2 AUD and attempt to resolder a new one in its place its good practice if you are a beginner to soldering it beats throwing it away without trying to fix it