Am I able to replace a motherboard's aux input?

There’s a tiny portion of exposed wire on the very edge of the broken green input.

I fucked up last night and moved my chair while my headphones got wrapped in the wheel without me noticing, the input still works but would there be a way to just replace it to prevent any future issue that may arise from this?

Its just a green rubber thing.

Its not that big of a deal really. And aside from finding the green bit and gluing it back on, IDK what you could really do.

As long as it didn't rip out the connector from the mobo then you should be fine and just shove the headphone jack back in there. may be a bit loose now though.

Use another socket , like the black one normally for rear speakers.

Windows audio or audio drivers for modern onboard sound (Realtek HDA?) should detect which socket headphones are plugged in.

Can do it in Linux too - need package HDA-jack-retask

You could always get an external dac/amp like a Fiio E10k or something. That would solve your problem and provide better audio as well (should you be interested in that sort of thing) .