There is no claim. There is no presumption of any claim. There certainly is no right to share a currency with the rest of UK the way many Scottish Nationalists believed there was. Such a claim or right only exists in the minds of those who believe they can force governance arrangements on independent sovereign states that are not their own. That this belief applies to many Scottish Nationalists is highly damning to any idea that they may support self determination in general.
Prior to the indyref, the UK government and main opposition party all accepted that if one party (Scotland) did not voluntarily wish to be in a political union with the rest, that party could not be compelled to do so against its will. The rest of the UK had precisely zero claim on, or right to preserve, the union. In the event of a yes vote, none of the unionist parties would be saying that the union was a "national asset" and that Scotland could be compelled to stay in it if it did not want to.
Contrast this with the shenanigans pulled by Salmond et al about currency union. Talk about hypocrisy.