when a router can't determine a path to a message's destination, where does it send the message?

When a router cannot determine a path to a message’s destination, it either sends the packet to a configured default route (often called a gateway of last resort) or, if no such route exists, it simply drops the packet.

Core networking idea

Routers look up each packet’s destination in their routing table and try to find the “best match” route. If they find a match, they forward the packet out the corresponding interface toward the next hop. If they do not find any matching route but a default route (0.0.0.0/0) or gateway of last resort is configured, they forward the packet there as a kind of catch‑all path.

If there is no matching route and no default route at all, the router has nowhere valid to send the packet, so it discards (drops) it instead of guessing a path or broadcasting it.

Mini Q&A

• “So where does it send the message?”
  • To the configured default gateway / gateway of last resort, if one exists.

* Otherwise, it does not send it anywhere; it drops the packet.

• “Why not just broadcast it?”
  • Broadcasting unknown traffic across routers would create congestion and security problems, so standard IP routing behavior is to drop packets with no valid route instead.

Information gathered from public forums or data available on the internet and portrayed here.