There is life at the bottom of the Mariana Trench however it's not regular types of fish like you see in the regular part of the ocean.
The creatures that live down in the Mariana Trench would probably creep you or some people out should you see them.
Some creatures that I know of that live at the bottom of the Mariana Trench are the The Ghostfish, The Barreleye, Fish or Spookfish, The Dumbo Octopus, The Goblin or Vampire Shark and the Giant Toxic Amoebas.
I've also heard that Sea Cucumbers live at the bottom of the Mariana Trench as well.