What I need to know is that, what does a certain website have to violate in order to get its domain removed completely from Google Search?

I am asking because I've seen websites infringing on DMCA protected content (Books, Movies, etc) having their domain removed from google, so they purchase another one and redirect the old domain to the new one.

But at the other hand, there are many websites of such type never got their entire domain removed from Search Results (Only infringing URLs got removed) although they've been running their sites for years, have a lot of popularity and there are tons of DMCA reports filed against them monthly.

So can you please explain how does Google behave in matters of domain removals?