ALL stores will close "immediately" and re-open under the management of the liquidation company. Yes, it will take 2-3 months to close a store (some will close quicker and consolidate merch to other stores) but the moment liquidation starts (on a massive scale) Sears/KMart will be no more.
Yes, a handful of people will remain at corporate to wind down the business, close out the books, etc. but it will be a skeleton crew from Day 1, and shrink weekly until the last few Finance and HR folks shut the lights off for the last time. But groups like Marketing, R&D, etc. will be gone days from the announcement as the new "owners" of Sears will look to maximize the amount they can get out of each store.
Liquidators come in quickly in the final stages, make an offer (usually 60 cents on the dollar) for the remaining inventory, and then they look to try to make a profit on that investment. While that happens, the rest of Sears will be auctioned off, and some company will get the names, trademarks, etc (likely for pennies of what it was worth 10 years ago) and that will be the end. The liquidation company will try to sell everything, even bringing in items that they got at other auctions to sell, and when they reach a certain inventory level, they'll put the remains in a warehouse for the next liquidation that they do.