It's not quite as simple as cash-on-hand, turnover, or profitability. Start-ups without revenues or net profits may be solvent if investment capital is available, premised on future profitability or a viable exit strategy. But it's fairly strongly related.
Airworthiness is more an overall assessment of risk.
A substantially compromised aircraft, with expert piloting and favourable weather, can still land successfully.
A fully-airworthy aircraft experiencing CFIT won't. Nor will one flown into unanticipated adverse conditions such as violent weather, volcanic ash, or wind shear.
And of course, a sufficiently crippled craft cannot be landed successfully no matter what.
(An additional case is of a landing with partial survival of passengers and crew. We'll omit that.)
Airworthiness increases he probability of a successful flight. It's neither strictly necessary, nor sufficient. It is part of the overall risk assessment, effectively a creditworthiness rating.
An airworthiness certificate is a specific certification of such airworthiness.
It's usually not a problem for a business to incur a short term operating loss.