While I seriously doubt that little chopped up pieces will sprout, I guess it's possible if you end up with all the correct parts still intact.
See the section on "leaf-bud cuttings" at the link below. It mentions 2 examples of the type of ivy that can be propagated from a leaf cutting, but you need more than just the leaf itself.
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I'd call my local cooperative extension for a more definitive answer based on my exact situation: type of ivy, climate, soil conditions, time of year, etc.
Dead, brown *and* dried out? I think you could have stopped at "Dead".
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