My husband is making barbecue sauce and putting chopped cooked onion in it. He made large amounts and stored some in mason jars and put them in the pantry; he put 3 squeeze bottles in the fridge. I'm scared the onion may spoil but he doesn't think so . Please help
Unless he actually canned the sauce (processing the jars in boiling water bath or pressure canner as appropriate) and was working from a trusted recipe, no, this is definitely not safe.
It takes processing like this to make canned goods shelf stable. And the recipe is important too; for example if the pH isn't low enough it's not safe to use the boiling water bath method. This isn't just because of the onion, it's the sauce as a whole.
The risk here isn't just that the food may spoil. It's that something unnoticeable will grow in there, like botulism, and it could make you extremely sick or even kill you.