Spesh and I both posted further up this thread about the possibility of Wrongful Trading.
As I understand it (I'm not a lawyer!), a company may trade whilst insolvent and be doing nothing wrong legally, if the Directors can show that they had a reasonable expectation that by continuing to trade the company would become solvent and bills are paid as they fall due, ie trade its way out of trouble.
However if a company is put into liquidation, the Official Receiver or more likely, an appointed Insolvency Practitioner can decide under s214 of the Insolvency Act 1986 that the company was wrongfully trading. The IP will look at whether bills were paid as they were due, the ratio of debt to assets, whether there are outstanding debts owed to HMRC/VAT, whether the Directors increased the debts of the company knowing the debts could not be repaid and so on. Wrongful Trading is not the same as fraudulent trading and no intent to commit fraud is required.
The IP will also look at the general conduct of the Directors in the period up to the liquidation!
If the IP decides that the company has been wrongfully trading then s/he can require the Directors to pay into the insolvency from their personal assets. However, due to IP fees etc, this is an expensive course of action so an Insolvency Practitioner is unlikely to go down this road unless the Directors have substantial personal assets to make it worthwhile going after them. But it does mean that if they have been wrongfully trading and do have personal assets then the Directors lose the protection of Limited Liability status.
A Director can also be disqualified for up to fifteen years if their conduct warrants it.
(edited for multiple typos..)