If you haven't finished something that's been sitting in the fridge for over two years, then it's not likely you're using it enough to waste the space in the fridge on it. Just ditch it. For ketchup, just ask next time you go ANYWHERE that has take-out service (including the supermarket deli area) for a couple of packets of ketchup. Keep them in the cupboard and throw them away after 6 months if you don't use them by that point.
For chicken base, it should have a sell-by date, which is not the same thing as a use-by date. Once it's opened, you can keep it in the fridge probably for a couple of months. And then throw it away.
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