The history of very wealthy people bringing down democracies goes back to Julia Caesar and Pompey bringing down the Roman Republic, and probably even further.
The question is, how to make democracy stable against interference by very
wealthy people?
One idea that occurred to me was to have non-linear money that becomes proportionately less valuable as it is accumulated into larger and larger amounts. Add $100 to $1000 and you increase that value by approximately $100, but add $100 to $1000000 and you only increase that value by say only $1. Of course this is impractical in this form, but this is in effect what progressive taxation does.
So maybe a democracy could be made stable against billionaires by having progressive taxation which prevents people from accumulating more than a certain proportion of GDP, say.
This would lead to a sort of capitalism in the small but communism in the large.
The revenue from this progressive taxation wouldn't even need to fed into the governments fund's, if its purpose was to supress billionaires then it could just be destroyed or 'burnt' and still achieve its purpose. Another possibility would be to distribute it to the citizens of the country as a sort of 'divident to shareholders', but you would have to be careful with this because some would-be billionaires might use this as a lever to build their popularity.
So a stable democracy would be a voting system plus an army (to prevent takeover from outside) plus progressive taxation (to prevent takeover from inside) plus a few other things to deal with things like citizenship and immigration.