While many sites claim to offer an "ISO" for The Last of Us on the PPSSPP emulator,

A: No. The PS Vita had a remote play feature for PS3, but no native ISO exists.

However, the spirit of the search is valid. You want mature, story-driven, survival horror on a portable device. The good news is that the titles for PPSSPP— Resident Evil: Revelations, Obscure, Silent Hill: Shattered Memories, Peace Walker, and Dead Head Fred —are waiting for you. They run beautifully, respect your time, and deliver that gritty, tense atmosphere you crave.