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add_action('woocommerce_add_to_cart', 'update_product_stock_on_add', 10, 6);

function update_product_stock_on_add($cart_item_key, $product_id, $quantity, $variation_id, $variation, $cart_item_data) {
    global $woocommerce;

    $product = get_product($product_id);

    $woocommerce->cart->cart_contents[$cart_item_key]['old_stock_quantity'] = $product->get_stock_quantity();
    $woocommerce->cart->cart_contents[$cart_item_key]['add_time'] = time();

    wc_update_product_stock($product_id, $product->get_stock_quantity() - $quantity);
}

add_action('woocommerce_after_cart_item_quantity_update', 'update_product_stock_on_update', 10, 2);

function update_product_stock_on_update($cart_item_key, $quantity) {
    global $woocommerce;

    $cart_item = $woocommerce->cart->cart_contents[$cart_item_key];

    wc_update_product_stock($cart_item['product_id'], $cart_item['old_stock_quantity'] - $quantity);
}