I'll add Parasyte: The Maxim here, it's about a modern day Japan which gets infested with Parasytes, organisms that seem custom designed to hunt humans. They start off as tiny, get into a person's body and if they get to the brain they eat it and take over a person's body. They're as smart as humans too so they kinda set up their own little communities and hunting zones. The main character is a guy who got infected with one but it never made it further than his right arm before it matured so he has zero control of his right arm and it can talk and use extremely lethal blade attacks.
It's psychological horror with plenty of action, it ends up as a story about how humans are actually the real monsters and shit (I think) but against the terrifying shit the Parasytes can do I think that line of reasoning is just bad. It's shown that a decent mid-tier Parasyte can clear a room of average humans even if they have swords and guns and they have an insect like mindset with practically no empathy. Then it tries some environmental commentary over the last 2 episodes and it kinda turned me off on it. Great series though.
Thanks for reminding me of Liar Game too OP, I wonder how much further they got after that massive hiatus it had a few years ago. I wish it got an anime.