If you use “ip unnumbered fas0/0” on your serial interface and your fas0/0 interface goes down then any packets destined for the that IP address will not be processed and OSPF will drop.
The packets are not processed by the interface per say, they arrive on the interface and then they are actually processed by the RP (processor). If the destination address is a down interface then the router should not process the packet. I have seen some weird behaviour though with this type of topology where only 50% of packets are dropped leading to strange results. Personally I would stay away from unnumbered unless you have a specific reason to use it, like in carrier networks.