1. The first option of course is to find another job and get a new TN before the closure.
2. if you don't find a job before closure, and you wish to stay in US for a while, you should file an I-539 requesting B2 status on your last day of work. Your TN is no longer valid after that date, so you should get a valid status (filing I-539 will keep you in B2-pending legal status). Then, should you ever get a new sponsor, go to the border (or premium file an I-129) and get new TN, or prepare to leave sometime in the next few weeks/months (you can collect EI only if you go back to Canada).
3. Leave and go back to Canada within a couple of week after closure, handing in your TN I-94 to Cdn border officer and apply for EI.