There is no way to remote save another user's edits before disconnecting them from the geodatabase, and as mentioned in the comments this would be a bad idea anyway as you'd potentially (probably?) introduce bad data into your featuer classes particularly if the data wasn't ready to be saved.
An example of this may be where features have been added or moved to aid editing but not actually permanent edits.
Another may just be that the user was never going to save the edits anyway.
While neither of these are really "best-practice" both have the potential to happen often.
Instead of disconnecting your users without notification, perhaps a change in the DBO process would be to notify users ahead of time that maintenance work is going to be carried out and that they need to be disconnected before a specified time otherwise they would be disconnected. Add that any disconnection means that unsaved edits would be lost.
Alternatively users could be contacted before disconnect to give them an opportunity to save and disconnect themselves.
This isn't just something that happens for geodatabases, it could happen for any type of enterprise database.