My suggestion is to add home security to houses (it's in house upgrades) so that for example if someone breaks into your house while you were offline, then you can see the logs of last 24 or 12 hours.
Hum... That would be usefull to track who robbed you. But what would that info be usefull for?
You cant get revenge since its more than 1 hour.
Maybe track who robbed you to steal from them?
Just pay insurance and dont live in Rich Street and most robberies wont affect you that much.
I don't really think this would be utilised and therefore isn't really worth the development time. Sorry. I have limited development time.