This is possible and a director can resign at any time and will lodge that information at Companies House as required. However, if a company subsequently does become subject to insolvency proceedings, and the resignation has happened at any time within the two years prior to the insolvency, the director would still be likely to face questioning from a Liquidator with regard to their involvement in the company, not necessarily because the liquidator believes there was anything untoward in their involvement and the circumstances of their resignation, but because a liquidator will have a duty to look at all relevant transactions in that period.
Resignation as a director and forfeiting of shares or transferring shares to other family members will not mean that an individual will escape all scrutiny in the event of the insolvent failure of the company. Indeed it will still the duty of the insolvency practitioner to file a return with the relevant government department on the conduct of that director and, if the government department feels it is appropriate, they may take action against that director or indeed the director may still be examined in court if necessary.
Forfeiting of the director title is not a quick or easy means to divest of all responsibility.
Were a director to ask another family member to act as director in their place, they may still be regarded as a shadow director, i.e. someone in accordance with whose instructions another person is accustomed to act. Therefore as shadow director they would still be subject to scrutiny and, more worryingly, they may find that a family member is also subject to proceedings by the relevant government department as somebody who has fronted for them.