Could they pick up the mined blocks and drop them upon death?
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"Colder than the snow that blankets the earth" "Colder than the ice that cover the stones and freezes the rivers" "Colder than the north wind blowing through a winter-bound forest" "Colder than all these is the smile of a Shade of the Dark"
Zombies already got numerous buffs, most of which make them quite annoying. And we don't need another mob that griefs, endermen already do that. On top of that, zombies don't have spades, axes, or picks often enough to make this a significant suggestion.