Yes Fuji, a simplification but true nevertheless. If a company has a "negative" balance sheet; that's insolvent. There are grey areas inbetween granted, but trading with the knowledge that you can't pay your debts is illegal. Simples.
Indeed, for that reason many companies are given legal protection while trying to re-structure their affairs
Indeed, it's called Administration.
This is what I do for a living after all
Cheers
Whirls