I don't believe this is possible.
The closest thing to this would be Priority levels which can be set to email the Tech, The Tech's Supervisor, or the Group Manager if some particular action is not taken within a timeframe, but that action applies equally to Open/Resolved/Scheduled/Assigned tickets. So, based on a Priority, i can email someone if a ticket has not been updated for, say...21 days.
You might think that you could accomplish this with an Action Rule...and you almost can. The problem is that Action Rules aren't able to cue off of a time directly. This is because Action Rules are checked when a ticket is updated. If the condition you are checking for is a ticket NOT being updated, the Action Rule will never trigger on that.