My sister made me a sandwich with onion on it. It was the best sandwich I ever had. She said she had to use a rotten onion and peeled quite a bit until she got to the usable part. I'm sold and wonder if chef's use this trick?
Of course if the entire onion is squishy I'd pass.
As soon as you get your onions home, take them out of the bag they came in and store them in a cool, dark, dry place. It may be better if they don't touch, but at least make sure that only healthy portions are touching. So inspect the onions as you move them into storage. The ones that are looking not-so-good, keep them in the front to use right away and don't let the bad parts touch the others. The good onions will store really well, whereas if they had been left in the bag and put en masse into storage, they would all go bad together relatively quickly.
I use slightly bad onions. Just cut off the bad parts and/or peel away the bad sections. The rest of the onion should be fine.
I keep my onions in the fridge. They keep forever. Never store onions in the same place with potatos. Someone said something earlier about that I think. The onions will cause your potatos to rot.
My left bottom fridge drawer holds onions, my right bottom draw holds my potatos. I seldom have to throw out either. I only purchase purple onions occasionally and never more than 1 or 2 at a time because they do not keep as well for me.