Take necessary meassures to prevent suspects fleeing from criminal investigation, judgement and continuing to commit crimes.

I wonder if you would misunderstand "prevent suspects fleeing from criminal investigation", because I didn't mean "prevent from", I meant "flee from"...
Hmm, your comment is more confusing than the sentence, which is pretty clear, I think. I would phrase it:

"Take necessary measures to prevent suspects' fleeing from criminal investigation and trial, and continuing to commit crimes. "-- meaning that you want to stop their flight from criminal justice and stop their committing more crimes.

Is that right? Is that what you wanted to know?
The wonderful symbol "'" has made the thing so clear!