Hi,
As per my knowledge, I don't think we have condition to provide as "If recipient not found then don't do anything". You may need customize in Alert Framework.
You can try these options:
Option 1. IMG -> Event Management -> Reactions to Event Messages -> Define Alert Framework Connection -> Define RFC Connection to Central Alert Server -> Give dummy RFC destination (check with BASIS team, normally client have configured dummy RFC destination not to trigger or process anything). I haven't tried this option, but you can try this config. You have to consult with your BASIS team as they may have other alert categories that should not impact.
Option 2. IMG -> Event Management -> Reactions to Event Messages -> Define Alert Framework Connection -> Define Alert Framework Integration to SAP Event Management -> Assign Alert Categories -> Provide Activity Param.ID (Which you given in rule set), specify your alert category, select INT Internet E-mail address in Communication Method and just give dummy email id or the email id which goes to internal DL list in Communication Data.
Last, schedule this program RSALERTPROC in background to delete old alerts.
Check and let me know.
Regards
GGOPII