How to access deleted term inside delete_product_cat action

You get 500 error, because you’ve added your filter incorrectly… It takes 4 params, but you register it as it was using only one.

add_action('delete_product_cat', 'sync_cat_delete', 10, 1); 
//  10 is priority, 1 is number of params to take

function sync_cat_delete($term, $tt_id, $deleted_term, $object_ids){
    var_dump($deleted_term);
}

So if you change that 1 to 4, it should be OK.