Like the other remnants of the British Empire, the British Indian Ocean Territory was never a part of the UK. It was just land that we (the UK) expropriated from Mauritius at independence. A just solution would be for Mauritius, as the (now) actual successor state, to control dot-io.

IMO what will probably happen is that ICANN "promotes" the zone to being yet another top-level non-country code domain like .biz or .horse etc. Which is effectively what it is now.

Edit to add:

I don't think the .su precedent is applicable here. The Soviet Union was an internationally recognised state with a population, military, Montevideo Convention duties, seat at the UN, etc. The BIOT was and is nothing like that.