Even if no one can use the wealth, wouldn't it be placed in some kind of trust in order to keep accruing wealth rather than be decimated by inflation?
And then, as the frozen rich wouldn't use any of their wealth, it would just keep accruing wealth. They would be perfect, frozen, capitalists. The control of that wealth would give power, and controllers of the trusts can gain even wealth and thus power more by coordinating. The power would only keep growing as more rich freeze themselves to keep up with and join the growing trust of trusts.
Living in a society where the frozen owners would own all the means of production, these frozen owners would naturally be hailed as sleeping kings in order to motivate me system. They may even be seen as something godlike.
Then one day, if one wakes up, it would cause immediate power struggles, as well as give a flash point for the discontent of the billions of impoverished serfs slaving away for the controllers. But the controllers would mobilise violence, and....
Oh, HG Wells already wrote this story. Typical!
Ah, this reminds me of an old book I came across years ago. Printed around 1920 it spent the first half with examples of how the future has been foretold correctly many, many times across history. The author had also made several correct foretellings, among them the Great War. Apparently he tried to warn the Kaiser.
The second half was his visions of the future including a great war...
Unfortunately it was France and Russia invading the Nordic countries in the 1930ies. The Franco-Russian alliance almost got beat thanks to new electric weapons, but then God himself intervened and brought the defenders low because the people had been sining and turning away from Christianity.
An early clue to the author being a bit particular was when he argued that he got his ability to predict the future because he was one quarter Sami, but could still be trusted because he was "3/4 solid Nordic stock". Best combo apparently and a totally normal way to describe yourself.