I worked in financial services for 12 years - I know my way around a balance sheet. I also dealt with many people who are quite happy to throw money at a business like Rangers for various reasons - none of them footballing.
Manchester United are run on dodgy loans originally obtained by leverging the club and its assests at a high interest rate. After they were restructured it's still a terrible deal for them. The owners dont' care, though, as they invested basically nothing, have zero risk thanks the asset backed nature of the loan, and all the while they skim off millions directly into their pockets.
Like them or loathe them (and I'm in the latter camp), Rangers have a world wide brand they can trade on - not as large as other clubs, but large enough that there are enough daft punters who will spend money on them.
Dave King saw the opportunity to make himelf some cash, and grabbed it. He'll be kicked out soon enough and another, slightly more honest backer will be found.
While it would be entertaining to see them go out of business, I just can't see it happening any time soon.