Preservative for pickles

Traditional fermented pickles were kept in barrels, but they're not the kind that you buy in a big jar at Costco. Those pickles have been briefly cooked in a brine, and should be refrigerated after you open the jar. The salt and vinegar should keep them safe for a while, but they will likely go bad at room temperature before you finish eating the whole jar.

As an anecdotal note, an office I used to work in kept one of these large jars of pickles around. After being open for a few years, they were clearly spoiled, and nobody would touch them.

is it solely by virtue of its acidic content?

Yes, not a lot of biochemistry is happy living at pH 2 - and the stuff that can live there is already happily living in your gut with a ph of 1

is there a kind of ratio (or other metric) of vinegar to know whether something needs to be refrigerated to keep from spoiling?

You mean foods already packaged in vinegar? It would depend on how well they had been cooked/sterilized before packaging and how strong the vinegar is. Industrially made pickles will be a lot cleaner than something you pickle at home, but store bought pickles are likely to use much cheaper, more dilute vinegar than your grandmother did.

what components can act to counteract vinegar's ability to preserve food?

Anything too alkali will neutralise the vinegar's acidity

can vinegar stabilize anything that otherwise would spoil?

Not necessarily, it has to be something where the vinegar can penetrate into the food - it's not going to preserve steaks as well as vegetables. And of course the vinegar taste is going to help if you are trying to preserve say strawberries! Also fungal spores can probably survive dormant in vinegar (if not grow) - fungal spores can survive dormant pretty much anything.