Hi Joe,
It depends on what level you want to monitor Endpoint health/liveness. One the Platform level you can use Heartbeats • ServiceControl Heartbeats • Particular Docs and Metrics • Particular Docs with Critical Errors • NServiceBus • Particular Docs. On the hosting level (kubernetes, …) you can use any monitoring feature provided by the host technology. Maybe the good idea is to have double guard and use both ways 
If you mean database deadlocked during message processing then NServiceBus kicks off Recoverability • NServiceBus • Particular Docs and should resolve this kind of transient problem. In the worst scenario the message will land in the error queue. After fix the issue you will be able to re-try failed message using Retrying failed messages • ServicePulse • Particular Docs
Hope this help.