The title of this post asks one question and the text of the post asks a different question. So perhaps 2 answers are called for.
1) the title asks what a router would do if it received a packet and can not find the destination address in its routing table. If there is a default route then the router would forward the packet using the default route. If there is not a default then the router would return an unreachable to the source.
2) the text asks what a router would do if it received an arp request with a broadcast hardware address and can not find the destination layer 3 address. There are several aspects of this question to address:
- in an arp request the hardware destination address is always a broadcast. So this is expected and does not change anything in how the router processes the request.
- if the destination IP address is in the local subnet it does not matter whether the router can find the address or not. The router does not send any response when the destination is local.
- if the destination IP address is remote then the issue becomes whether the router has enabled proxy arp or not. If proxy arp is enabled and if the router believes that the destination address is routable (either through a matching subnet in the routing table or through a default route) then the router sends an arp response and in the response the router supplies it own mac address. If proxy arp is enabled but the router finds that the destination address is not routable then the router does not respond to the arp request (there is no unreachable) and the arp request just times out.
HTH
Rick