A switch that can report unavailability in a label-switched network is provided. During operation, the switch can determine that a label-switched path is unavailable for forwarding a packet. The switch can then generate a notification message for collecting unavailability information at a respective upstream hop of the label-switched path. The notification message includes a depth indicator indicating the depth of collected unavailability information and an ingress label of the packet at the switch. If the switch is an intermediate switch on the label-switched path, the switch can forward the notification message to an upstream switch on the label-switched path, thereby allowing the upstream switch to collect further unavailability information in the notification message.