Gerry Adams is an Irish member of the UK Parliament. He wants to stand in the upcoming Irish election, so he has sent a letter to the Speaker of the House resigning his seat. The problem is, he can't. Back in 1624, Parliament - then a very different institution - passed a motion that being an MP was a sacred trust which could not be voluntarily given up. And so Adams cannot simply resign, and may be forced to keep his position as an MP, even if he doesn't want to and never turns up.
There's a way around it, of course: in addition to the usual exits of bankruptcy, insanity, serious criminal offending or death, MPs are automatically disqualified if they accept an "office of profit" under the crown. So traditionally MPs have circumvented the ban by being appointed to a royal sinecure. But Adams is an Irish republican, who has refused to swear allegiance to a foreign monarch to enter Parliament, and who will not do so in order to leave. An attempt by Downing Street to automatically appoint him met with a refusal and the government was forced to apologise. And so Adams is trapped by the UK's archaic constitution in a job he does not want and will no longer be able to perform.
It is utterly bizarre that a supposedly modern democracy continues to operate in this way, and it highlights the desperate need for the UK to modernize its constitution. But given that they're still struggling with concepts such as equal-size electorates, and are still using an unfair electoral system, that doesn't seem very likely.