I have a dedicated ‘onion’ jar: glass, with a metal lid so I don’t have to worry about it retaining odors OR allowing them to get out in the fridge. I believe that it originally held jumbo olives. Short and squat with a huge opening, it’ll take most onions.
When I have a left over giant purple olive I use one of the regular plastic storage containers then toss it afterwards. I get them all the time with lunchmeat in them, so no loss.
I use a newspaper to completely eliminate any onion smell getting into the fridge. I wrap the onion in plastic wrap, cover that in a piece of newspaper, and put it in a baggie. You won’t be able to smell it at all.
I dice the whole thing, toss the unused portion into a ziploc freezer bag and whenever I need some more onion, I pop open that bag, dispense some frozen onion. Done.
I started doing this when I realized I was spending money to buy frozen “seasoning mix” which is onions, celery and green peppers all diced up in a bag. Hell, I can do that myself! I started doing exactly that.
How do you really have half an onion around for more than a few days at most?
Damn near every recipe uses onions- we’re far more likely to run out of onions than have a quandary about how to preserve part of one for later use. The idea that half an onion might actually lurk around in the fridge without being used is kind of a bizarre one to me.
That said, when we do only need half an onion, it just goes into a ziploc bag with the air out, and stored in the fridge for a few days until we need some more onions.
Coincidentally, I just happened to watch the How It’s Made episode on onions:
Concerns about bacteria are brought up twice, at 2:15 (onions with their ends cut off are rinsed with ozonated water to kill bacteria) and again at 3:27 (chopping an onion releases a lot of juice that apparently provides a good medium for bacterial growth).
I just cut it crosswise, skin on, and the part I don’t use, I place cut-face down on a plastic lid and set it back on the shelf in the fridge. It will keep just as well as a whole onion, since the face-down surface gets no air exposures. This works great for apples, too, and lots of other things. Good for several days, I presume you’re not talking about any more than that.
If you’re worried about bacteria, just be sure to use a clean knife and plastic lid, and don’t touch the surface with your hands.