If the Sun became a black hole (which would NEVER happen, but let's use our imagination), we wouldn't fall into it. The Sun-turned-BH would be less than 4 mi across, but it's gravitational pull on Earth would remain the same. The Earth would continue moving on its normal orbit.
So, yeah, we'd all die because we wouldn't get any more sunlight, but we wouldn't fall into the black hole!
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