“Find to her cost” [closed]

Woe would befall anyone who sought to sully the good name of Windsor dynasty, as Daisy Warwick, one of Edward VII’s mistresses, found to her cost.

The whole context is such:

Woe would befall anyone who sought to sully the good name of Windsor dynasty, as Daisy Warwick, one of Edward VII’s mistresses, found to her cost. Daisy Warwick who probably was the most important of Edward VII’s mistresses, told the advisors that she is going to publish a large amount of letters, she was trying to blackmail George V. She wanted to be paid 100,000 pounds. This provokes total panic amongst the Royal advisors. Effectively, what happens is that the Royal solicitor serves her with a sort of notice that she’s going to be committed to Holloway prison unless she shuts up.

What does found to her cost mean, and what might be the grammatical structure?

It is an idiomatic expression meaning:

to someone's cost:

With loss or disadvantage to someone.

• ‘without programmes to play on it, the cleverest machine is useless—as some hardware manufacturers already know to their cost’

Also: at someone’s expense

ODO

"...as she learned, to her detriment."

She found out that it was a bad idea, and "to her cost" means that the learning of that lesson cost her something. You can find equivalent phrases using "surprise", "dismay", "consternation", "chagrin", and "detriment". It might be a shortening of "...leading to..."?