Sugar, honey, and jams have such a high concentration of sugar that they will pull water out of any bacterial/fungal cells that land on them, as sugar is hygroscopic (it sucks water out of whatever is around it). The cells, without water, cannot survive, so they will die.
Over enough time and with enough water, the sugar will not longer be able to pull that much water out of the bacterial cells, meaning they can survive and reproduce. So the food must have a very high concentration of sugar in order to last; lower concentrations will go bad much more quickly.
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