An ARP request is made to know the MAC address of the device that has some specific IP assigned. This way we will be able to know what MAC address we should set to send out IP packet.
If a device wants to send a packet to another device in an external network, it first looks at its default gateway's IP address, then it makes an ARP request to know the MAC address of the device that has the gateway's IP address assigned, and then sends the IP packet using that MAC address.
Let's say that we didn't have any default gateway ip address configured in the device that wants to send IP packets. Let's say the router didn't have any IP address assigned either. But the router has an entry in its routing table entry to redirect the packet that the device wants to send. Then...
- The device sends an ARP request asking which device has the IP address of the packet that it wants to send.
- Even though the router itself doesn't have that IP address assigned it should answer with its own MAC address anyways because it can redirect the IP packet to the correct destination.
I haven't made a proof of concept to see if the router would actually behave as I said or not, but I have understood that the router just won't answer to the ARP request in this case. Why though?