I freeze half jars of marinara sauce, because they only keep 3-5 days once opened. They're very acidic, but there aren't really any preservatives in them (which is a good thing).
I have a very weak stomach, and I do not play around with food safety. My dh will sometimes eat things the day (or day after) that I would throw something out, but even that is about his limit. It's not worth being sick for a few days to a week or more and incurring the ER bill IMO. (I realize not everyone would have to go to the ER, but everytime that I have had a stomach bug of any sort, I get so dehydrated, that I have to go in for fluids at a minimum, if not stay a few days).