RLMT after Tier-4 expired

Hi all!

My Tier-4 visa expires on the 25 January 2017. The employer is only able to issue a CoS in early February. Can they issue an unrestricted CoS during the 14 days after the expiration date or they have to run a RLMT?

If they have to do the RLMT, should I leave the country before the 25 January to avoid being an overstayer or staying for a few more days (until 1 Feb) will not affect my future applications?

Many thanks!