Readers' forum - Death and taxes

I have a lot of clients who are 'one man companies'. If they are the only director of their company what happens if they die while the company is still in existence and trading? It occurs to me that there is then no one to look after the company's affairs.
Should such a director appoint his or her spouse as a director just in case; and if he does are there any tax and other implications that he should be aware of? I should be grateful if readers have any comments on this suggestion or any alternative suggestions on facilitating tax and administrative matters on the death of a sole director.
                                        — Reaper.

Reply by Bella:

Reaper is right to be concerned about who looks after a company's affairs if the sole director dies in the saddle; but the company is not dependent...