When White people lose, I suspect Jews will claim to be the only Whites

I'm not so sure about that. Right now they pretend to be white in order to subvert our societies. In doing so they have repeated to every single nonwhite minority that White people are bad and everything associated with them is bad. So once all the real White people are dead/enslaved, pretending to be white would actually be a pretty bad disadvantage for them because it would make them a target for every 65 IQ Muslim/African with a grudge.

They are already feeling the effects of this with Israel's reputation at rock bottom among libtards, most of whom are either self hating Whites or envious nonwhites. A big reason why their reputation is in tatters is because jews, particularly Ashkenazi jews, have pale skin, and the whole world just saw a bunch of pale skinned people genociding a bunch of brown Palestinians. To a libtard/nonwhite who can't tell the difference, that looks like another "whyte peepo is killing us to keep us down" mythos to add on top of all the rest.

Non-Western societies are far less tolerant of jews than we are. Some of them are ambivalent, like Brazil, but others like Iran or China or Egypt are not going to just let them stroll in there. If the West falls, Israel will be alone, and jews outside of israel will have to cloister together behind high walls, because every Western country will turn into South Africa.