Insolvency is simply being unable to pay liabilities. However, it is necessary to differentiate between simply having liabilities of greater value than assets, and actually being in a position to meet obligations as they fall due.
If a company has liabilities on its balance sheet that are of greater value than its assets, then it is technically insolvent. However, it may have cash flows that are sufficient to allow it to pay liabilities when they actually become due. The same may happen to an individual (or partnership).
If, however an insolvent company does not have the cash to pay liabilities, then its insolvency becomes a more serious matter, leading to re-structuring or liquidation.
A similarly insolvent individual may enter into arrangements with creditors, or become Bankrupt