If a company has a "negative" balance sheet; that's insolvent.
It is.
However, it may be insovent because it cant pay back its bankers or directors who are never the less happy to proceed under security of a PG or take the risk they may never see their money again.
It may have an excess of assets, but be unable to manage its current liquidity - just as serious as being totally insolvent.
It may also be solvent on a going concern basis, but just wait until the break up value of the IP, goodwill, stocks, debtors and FA has been realised.
There is a danger in allowing forumites to believe that assessing the state of health of a company is as simple as you suggest.
I have seen businesses that have traded successfully for 50 years or more eventually throw the towel in for reasons beyond their control and which they could not have reasonably forseen. They paid their taxes, they employed 100s of people, they ran a sound business - immoral that they went bust and owed some money - I dont think so - illegal - certainly not.