The service continues to run, but you'll see missing table type errors in the logs. The only caveat to that would be is if the table is missing and the service is turned off. When you got to turn the service on, it will throw an error and not run.
ArcGIS Monitor to can help you with this and/or writing a custom script to pull the error logs looking for such an occurrence. In my org, I control the DBs connected to the rest services. Outside of my automated publishing processes, no one can accidently delete something which cuts down on issues like that. Every once in a while there is an accident or someone doesn't update their service, but it is pretty easy to track down.