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Old Vinegar
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For more on marking an answer as the "Best Answer", please visit our FAQ.It should be fine provided there is nothing added to it (such as sprigs of tarragon, garlic cloves etc).
Vinegar is unaffected by bacterial decomposition as bacteria cannot survive in the acidic conditions - hence its use as a preservative in the pickling process.
The ethanoic acid ('vinegar') molecule is pretty stable, so will not readily undergo chemical decomposition, although alteration of some the congeners may occur over time, especially if left on a sunny windowsill. Congeners are the constituents that occur in small concentrations that give a vinegar (such as malt or red wine vinegar) its colour and taste characteristics.
Analagous to this, is sugar. Again, it has no 'use-by' date, as it will last indefinately. Again the sucrose molecule is stable, and bacteria, as with acids, can not survive in high sugar concentrations. Hence its use in sugary preserves (jam etc) and fruit preserved in syrup (ie sugar solution). Sugar will, however adsorb other smells, so don't store it next to your onions !!
Until a few years ago, cider never had a 'use by' date', either. But I never managed to leave a bottle of the stuff around long enough to see what it was like after a few weeks, let alone a few years.
The vinegar would have been just fine! Had you found a jelly-like mass at the bottom of the bottle this would have been even better, for it is the substance called a 'mother vinegar', which you use to make your own vinegar by adding wine to it in a jar! Just like when you used to make a ginger-beer plant ..... if you're old enough to remember such things!