Critically, the core business is actually marginally profitable and they decreased their net indebtedness by around $500m over the year and increased their revolving finance facilities to over $7bn (access to money if they need it, Moody's am cry). A lot of the losses over the last few years have been paper losses, asset impairments, DTA write downs and such. What that means is money either spent in the past or in the case of a DTA, the asset taken on for tax losses carried forwards, are now being written off as they are not going to get that money back. They spent the money, previously and now they won't get it back through their normal operations.
It is a huge difference to a company that actually loses money outright where their normal operations cost more than the revenue they generate from sales. Nintendo are in this category which is why their situation seems worse than Sony's and they don't really have a clear path to recovery like Sony (getting rid of the TV division) because their problems stem from deeper issues such as smartphones killing their handheld business and being stupidly uncompetitive in the home console market.
For all their current faults, Sony still have a profitable smartphones division, a hugely profitable financial services division, their content division (pictures+music) reliably makes $1bn per year in operating profit and their games division seems to be recovering very nicely after the PS3 caused so much turmoil. In essence if they jettison the TV division they would be pretty healthy and though they would hold a significant amount of debt but they would be profitable, more than enough to redeem bonds and meet their financial obligations. I guess the issue is that it has cost Sony $1.7bn to exit PCs and I expect the cost of exiting TVs would be double because all 30,000 employees would need paying off and the losses on current stock and contracts would need to be written off.
Essentially, though it is true they lose money, a lot of it is on paper, and the core business is generating cash.