During a 90s election in Algeria, a radical (and popular) Islamist party made it clear that if they won, their first action would be to cancel all future elections.
This basically put all the secular parties (both left and right) in a bind. Do you just proceed with the election as if everything's normal, even though it might be the end of democracy if the radical group wins? On the other hand, if you decide to boot out the radicals from the democratic process, haven't you now ended free and fair elections?
Which is the solution. Bind themselves and everybody else.
Have a constitution that enshrines the right to things like fair elections and free speech. Have an amendment process that requires two thirds of the Senate, in a Senate that only has one third of the seats up for election in any given year. And three quarters of the states, which rarely agree on anything. Things like that.
Then even if the populists get in once, they don't have the power to end elections or free speech. And once the people see their true nature, they lose the next one.
Obviously you do have to be very careful not to allow any end runs around that process.
Because extra-judicial persecution of "bad people" [0] is something Popper never discussed or advocated for in _Open Societies and Its Enemies_. He very specifically advocates for this only when all else has failed, and only by the state itself -- being as such action doesn't bode well for any liberal democracy that undertakes such action.
I know you've not read the book, but perhaps read the Wikipedia article you're citing.
0. I've seen a whole range of people called "bad people" by antifa types these days, from centrists all the way to white supremacists.
it’s also called the paradox of tolerance, where if a society is tolerant of intolerance, eventually the intolerance will win by taking advantage of tolerance
https://en.m.wikipedia.org/wiki/Paradox_of_tolerance