Amazon would eat TRU's lunch if they went online only. Sure, closing the brick & mortar stores and selling off that real estate would help their balance sheet. But Amazon has been building their online infrastructure and distribution network for a long time. And Amazon's diversity of product ranges helps them if one sector falls short.... like toys.
I'm pissed at how TRU let themselves be saddled with all of that debt. And I'm really hopeful that a buyer will come along and see some way to transform the business, restructure their debt, and find a new way to can continue on. Hell, maybe Amazon can do that, too. They have the cash. And they already have a significant portion of the toy market. They're working at competing with WalMart in a big way, especially since WalMart bought a significant online retailer like Jet.com. Amazon took an inroads into brick & mortar retail when they bought Whole Foods because they saw value in that business, and a way to incorporate the store locations into their distribution network. This could be another way for Amazon to use TRU in a similar fashion, along with having a place like the R Zone to offer up their own electronics.
There will always be a market, because there will always be kids.