RE: Right but did this go to the debt or the assets?
You are mixing a few things up. To make things more simple lets assume he used 100% cash. So ESL wrote a check for $5.2B to SHLDQ. In exchange SHLDQ gave him the $7.55B in assets. Why would he get a deal like that? Partly because there was no other bids. Partly because the judge determined it was better for everyone than a complete liquidation and partly because some of the assets are intangibles (like the brand names) and therefore generally worth a lot less in a liquidation. As well the balance sheet you provided doesn't have a specific date and their year end is Jan 31st so it might have been for the quarter before and the assets might have decreased since then.
Back to the numbers. So the $5.2B goes into the SHLDQ bank account and is now a liquid asset. The $11B debt is still with SHLDQ. (you don't add the liabilities and assets together at all, they are opposite things, you subtract them so there is no $18.55B total). The judge (because this is in bankruptcy) then decides on how the cash will be doled out to satisfy the creditors (the $11B). Once that is complete the assets will be $0 and the liabilities will be $5.8B (because they were paid with the cash). If part of paying the creditors they agreed to forgive some of the debt (which is likely) then it would go down and ideally to $0 (in which case it becomes a clean shell). However that seems to impact the NOLs as well and would wipe them out. (I don't think that would be the case but its certainly possible)
In this case it was not all cash but other considerations as outlined in the purchase agreement. Assets and debts depend on how you look at them. If you sell something on credit that is an accounts receivable asset to you but to the person you sold it to, its an accounts payable debt. Its the same thing from the same transaction but depends on which side of the transaction you are on as to its meaning.
Make more sense now?
BTW, you made a post about me not providing backup or proof and of some holes in my points. Maybe I missed something and I have tried to consolidate posts as much as possible. If you wouldn't mind posting what I have not addressed in a single post and I will try to address it. Here is one you might have mentioned in simplified terms.
An NOL is a credit against future (or 2 years past) profits for tax purposes. So say you make $5B in profits in the future. If you have $5B in NOLs then you pay no tax on those profits. Awesome. The maximum corporate tax rate is 30%, in general its lower than that but I went with the max. So if you didn't have the NOLs then you would pay 30% tax on $5B or $1.5B. So you saved that money and therefore that is what the NOLs are worth. They are worth at most 30% but are only worth whatever your corporate tax rate is which may be lower than 30%.
I don't know what proof I can provide of this without pointing you to the entire US tax code.