Of course if you signed off with ATC (ATSOCAS or CAS) you are no longer in receipt of a service from them. And by implication, you are no longer in receipt of an alerting service either. But as long as you are in receipt of a service, it should include an alerting service.
For example, you are talking to London Info for a Channel crossing. You've got a Basic service, which implies an alerting service. You've told London you'll be at the FIR boundary (or coasting in, or whatever) at a certain time. When that time comes you don't check in. And you haven't checked in with London a few minutes later either.
At that stage London is supposed to do something. Of course their first action is not to hit the panic button and scramble all SAR assets, but they will try to raise you first on their frequency, then on a few other frequencies you might be on, then inform D&D so they can maybe replay a radar track, and so forth. That's what the alerting service is about.