This is extraordinarily far-fetched. Scotland seceding would leave the United Kingdom with a technically-inaccurate name, but not wipe it out completely.
I don't think there's anything unreasonable about British citizens in Scotland retaining this status alongside a new Scottish citizenship. Why should there be? It makes a mockery of the concept of close relations and shared history and so on if Westminster's reaction to independence is to unilaterally strip millions of people of their citizenship as what, a punitive measure? What then of all the British citizens who've emigrated to the likes of Australia and Canada and New Zealand and the US and been naturalised in those countries? Should they be deprived of their British citizenship because they don't need it anymore?
Your example of the dissolution of the Soviet Union isn't fully comparable because it happened has a result of a trilateral declaration by the three primary republics (the Russian Soviet Federative Socialist Republic, the Ukrainian SSR, and the Byelorussian SSR) that the union had ceased to exist. This did entail the end of Soviet citizenship, but since all Soviet citizens formally also held the nationality of their constituent Soviet republic all that was lost was the top layer, similar to how citizens of the EU are formally citizens of their member state.
Its really not far fetched. "RUK" would be the United Kingdom of England, Wales and Northern Ireland. I think Northern Ireland would leave almost immediately, Wales may or may not stick with England. That is more or less the Soviet Union break up situation. Even if Northern Ireland and Wales stick with England the primary UK successor state will start to redefine itself and that will eventually include Citizenship. Stripping Citizenship from millions of people is exactly what happened when colonies went independent, including Hong Kong in 1997. Its the absolute norm for states to only have citizens born or naturalised within their boundaries or children (some times grandchildren) of them. In the long term the best Scots without a link to other parts of the former UK would get, would be a BNO (Hong Konger) style travel document issued by the English (or Anglo-Welsh) Government. Irish independence was a century ago, it became a dominion first and the UK stayed mostly the same, it lost part of one of its 4 members. Thats different to all of its second largest member leaving. If England ends up on its own it will certainly create English Citizenship and limit that to people born in England, naturalised as a Brit while living in England or people with English parents. Why would England (or England and Wales) on its own have Citizenship determined fundementally differently to Scottish Citizenship? Especially if that overwhelmingly favours non residents of England (or England and Wales)?
In answer to your question about British emigrants, yes if they or their parents were not born in whatever was left of the UK (probably just England). A Scot who has already emigrated to Australia would be a Scottish Citizen (by birth right) and (probably) an Australian Citizen by naturalisation. Why would they be English, Welsh, Anglo-Welsh) or Northern Irish? Britiain and British will only be little more than geographical and cultural concepts if Scotland becomes independent. That is not necessarily a bad thing but it will quickly become the reality.
Irish unity is different to Scottish independence because Britain would more or less continue as is, and arrangements for a few hundred thousand unionists in NI can be made. If Scotland goes it effectively creates two different countries (if not quickly three + a united Ireland).
I do think its overwhelmingly likely that FOM across the four nations would survive the break up of the UK but on the basis of reciprocal agreements for each others Citizens. Of course many residents of Scotland were born in England, Wales or Northern Ireland (or one of their parents were) and vice versa so there would be many dual citizens with different combinations. Scots can't break away and expect the three other parts of the UK not to move on too!
@Journeyman for instance would have English Citizenship by birth, Scottish by long term residency in Scotland at independence and Irish Citizenship through a grandparent. There wouldn't be a Britain to be a Citizen of!
As an Englishman a major plus side of the breakup of the UK would be the oppertuntity to redefine ourselves a step removed from the legacy of the UK and its former empire. Being a Citizen of a mid sized global state (England) would suit me fine...