To unlock the Surviving isn't Living trophy in Days Gone, you will need to rescue 10 survivors. This will likely come through natural progression as you make your way through the story.
You will come across survivors as random events in the open-world. They can be found by listening for them crying for help. Once you rescue a survivor from Freakers or other humans, you can send them to a camp to earn trust/money.
Once you rescue the 10th survivor, the trophy will unlock.