If the company is insolvent and unable to pay all of its creditors in full, it should be immediately placed into voluntary liquidation by the company directors. If the directors delay they could become guilty of insolvent trading which has serious implications for the directors. One might also choose to appoint a liquidator when there are serious disputes between directors and/or shareholders that are likely to adversely affect the company’s ability to continue trading (this is known as a Provisional Liquidation).
If the company is not insolvent but the directors wish for it to be deregistered, a liquidator can be appointed to oversee a “solvent liquidation”, which is essentially placing the job of realising the company’s assets and paying out the debts into the hands of a registered liquidator. Alternatively, the company can pay out all of its debts itself and then simply apply to ASIC to be deregistered.