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It's not a particle in the regular sense you might know, like an electron. The pair that comes into existence is meant to annihilate immediately (meaning there's zero energy gain or loss) but because of where it appeared it can't.
When it appears as I described, there suddenly exists a real particle in the universe outside the black hole, so the universe gained +1 in energy.
But energy can't be created or destroyed, so that +1 means somewhere there must be a -1. And that somewhere is the black hole which caused the particle to exist in the first place by swallowing its pair.
It's not very intuitive, that's the fun part about quantum mechanics: nothing is intuitive.