An empty search result is a moment where the visitor has clearly expressed intent (they searched for something) and gotten nothing back — the single highest-leverage place to suggest alternatives, correct an obvious typo, or surface popular items in the category they were searching.
A nice illustration is fine, but it's not the thing doing the work — a clear, specific action ("browse bestsellers," "try a broader search," "here's what's in your recently viewed") is what actually recovers an otherwise lost visitor from that dead-end moment.
Most stores have never actually looked at what their zero-results search page or empty cart page says, because almost nobody intentionally designs them — they're whatever the theme shipped with by default. A ten-minute audit of every empty state on the site usually finds easy wins.