Canceling Support for old app Lets assume that I have apps that I have on offer on the Apple App Store. Again, lets assume that I no longer want to support an app and that I am removing the app from the app store. 

If my app no longer works or functions correctly after dropping support, is there a way I can suggest deleting the app or are their penalties for having apps that behave this way?
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From the looks of it though, it is pretty generic protect Apple and Apple's Brand and Good Will. If you received any additional agreements when your app was approved to go on the App Store, then review them as well.
From the looks of it though, and from wha articles in trade publications indicate, many developers just walk away from their apps.
As it sounds like you are trying to do the right thing, hypothetically of course, I do recall that one app that I had, Catch Notes, did post a notice to their landing page on the App Store that their product was no longer going to be supported. If you are able to make updates or adds to the page, then that is likely the place to do it. Also Catch Notes no longer appears on the App Store, so there is some process for removal.
Here are some news reports that made the tech sites.
Engadget
CNET
Techcrunch
Check with an Apple representative. There may be a way that the app can be frozen from future downloads, to allow sufficient time for the app's page to be seen by the current user base without expanding it. It is also possible that they are able to message your user base through their records of the App Store purchases. If there is security risk and you feel that the users should completely remove the app, then this is the right thing to do.