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When a packet's Time To Live (TTL) reaches zero, it is discarded by the router that processes the packet. The primary purpose of the TTL field in the IP header is to prevent packets from circulating indefinitely due to routing loops. Each time a router forwards the packet, the TTL is decremented by one.

When the TTL reaches zero, it indicates that the packet has reached the end of its allowable lifespan in the network. To provide feedback to the sender about this situation, the router that discards the packet sends an Internet Control Message Protocol (ICMP) message back to the originating host. This ICMP message is generally a "Time Exceeded" message, which informs the sender that the packet could not be delivered because it exceeded its TTL limit.

Other options present scenarios that do not align with standard networking behavior regarding TTL. For example, storing the packet in a buffer, logging it for analysis, or forwarding it to the next router would be contrary to the purpose of the TTL, which is specifically designed to terminate packets that are no longer viable for delivery.