Toys-R-Us has something of a unique IP as it is a toy store, and there aren't many of those, and Jeffrey the Giraffe has major bank as well as a cache of good will. You could easily rebrand TRU as a one-stop-shop for games, toys, online games, video games, action figures, comics, etc. and compete against Amazon by making it easier for people to find such things easily and ThinkGeek by expanding the focus. If TRU nails shipping turn times they could hold their own, especially as the local comics and collectibles brick-and-mortars are failing left and right and it is getting harder to get access touch collectables.
Sears is no different than Target, Kohls, Penneys, Walmart or any other retail store. Their branding offers nothing unique, and frankly the only major selling point Sears ever had was their massive mail-order catalog. which was iconic back in the day. There is literally nothing Sears offers that a half-dozen other entities don't also offer and Amazon is the Sears' catalog of the 21st century.
The only people who will benefit from any kind of Sears "resurgence posy BK would be the high level executives and whatever vulture capitalists are attached to the effort in hopes for a quick cash out.
If you are a working manager, supervisor or employee, your future, your livelihood, is not sustainable at Sears. Don't gamble on a pipe dream.