The signs that a company is insolvent are:

Liabilities exceed assets (balance sheet insolvency)
Debts cannot be paid when repayment is due (cash flow insolvency)

Choices
The choices available to an insolvent company are:

In-house Recovery Plan
Company Voluntary Arrangement (CVA)
Administration
Liquidation
Receivership (A declining option)

Wrongful Trading
If a company is insolvent its directors are duty bound to behave responsibly to protect creditors and shareholders interests. If directors are judged to have behaved unreasonably they can become personally liable for company debts from the time it became insolvent. This usually involves continuing to trade while insolvent to the further disadvantage of creditors.