Democracy is rule by the people, but one key question is 'which people?'
If one believes in a principle like 'no taxation without representation' then there's no obvious justification for restricting the franchise to citizens. Immigrants pay taxes, so perhaps they should be enfranchised too. Indeed, it might even be necessary to extend voting rights to non-resident foreigners too, if they are subject to taxes.
Those working on this issue are often interested in laws that claim universal jurisdiction - that is, they are not restricted to the territory of the state in question, but purport to be binding (on citizens or even people generally) wherever they are.
I noticed an interesting example of something like this in this BBC article about Iranian headscarves. According to the article, "Women in Iran are required to wear headscarves in public, even when abroad" but this obviously doesn't make much sense. If an Iranian woman is abroad, then she's not in Iran. Thus, the law doesn't apply only to women in Iran.
I'm assuming this law applies to Iranian citizens, though perhaps it applies to all women ordinarily resident in Iran. In any case, it seems that they can commit an offence outside Iran.
