Maybe we should not, but we toss taters and onions in the fridge.
Onions never last very long around here. Seems every time we are going to cook almost anything we work onions into the dish.
As for potatoes, several years ago a neighbor, who grew them, left a bag of small ones,less than the size of a half dollar around, on the doorstep for us. We tossed them in the veggie bin and forgot about them for about four months.
When we found them they were a tad on the soft side, but decided cook them up anyway. If they were bad, we would just have tossed them.
They were so sweet and tasty that every once in a while I toss some small ones in the basement fridge and forget about them.
They always turn out very well when we find them again.
Anyway, just MHO. Take care.