With some settings you could do that with the Autocloser plugin.
Settings group 1: Open tickets with no activity for 14 days, send notice and change status to Pending (make a new status for this)
Settings group 2: Pending tickets with no activity for 7 days, send closure notice and change status to Closed.
If they get to Pending it won't automatically put them back when/if they comment though, you could try using the status option "allow reopen" and select Open as the new status for it. That might work, haven't tried.