This topic is has kind of be inspired by Iron Corsair's Topic The Loyalist Traitors. I'm sorry if this topic has already been covered. I couldn't see it anywhere

I wanted to know what happen with the marines in Traitor legions who stayed Loyal to the Emperor.

I know from the first 3 books that Loken and other Sons of Horus became Lunar Wolves and died on the planet (the name escapes me)along with the Emperor's Children, Death Guard and World Eaters.

I also heard that some of Marines that did escape started the Inquistion, Is this the case?

It is certainly hinted that some loyalists from the traitor Legions (specifically those with psychic powers) were used by the Emperor in the foundation of the Grey Knights and/or Inquisition (this may or may not have included Garro of the Death Guard). Have a look here for the relevant quotes and discussion.

Apart from that, the fate of any other loyalists from the Traitor Legions remains unknown. The (few) marines that escaped from Istvaan on the Eisenstein, and any others who managed to escape the 'purging' of the Traitor Legions, may eventually be covered by later novels, but until then we just don't know what happened to them.