The particles do annihilate, but they don't have to annihilate with each other. If an electron/positron pair appear, the positron can annihilate a different ele

The particles do annihilate, but they don't have to annihilate with each other. If an electron/positron pair appear, the positron can annihilate a different electron, in which case the electron appears to jump. So if the pairs appeared light years apart, the antiparticles would annihilate something nearby, leaving their partners in the sun, as if particles were spontaneously jumping from all over the universe into the sun. Preposterous, yes, but as far as I understand, not actually impossible.