Hi,
I did not get the context exactly. But I would suggest some ways to achieve it.
1) If weblogic is monitored by APM, you can use 'Agent Connection status" supportability metrics to monitor the status of agent and alert accordingly. When I say agent connected status, agent will go down only if application server goes down. So either of case is true to check application server status as well.
2) Use EP Agent to monitor weblogic server logs(log monitoring plugin) for SHUTTING DOWN or something similar and report this to introscope. Use alerting mechanism to alert based on the data produced
3) We did this years back. I don't remember exactly but I can shed some light. I hope JMX metrics in weblogic relays the application server status(STOPPED,STARTING,HUNG..etc..). So your java agent which is monitoring weblogic app server will get JMX metrics as well. Use this JMX metrics(not sure exactly how to configure to get app server status, but it can be done) to know the server status and alert accordingly
Hope this gives some clarity and ideas. The Java agent documentation/EP Agent document will give a detailed idea for you.
Thanks,
Karthik