In ST:TOS 1x28, the USS Enterprise followed time ripples to their source from millions of miles. McCoy injected himself a drug by accident and beamed down to the planet in an out-of-control situation.
Kirk, Spock and 4 more crew members also beamed down to search McCoy. On the planet's surface, they found an intelligent entity (The Guardian of Forever) which apparently was the source of the time ripples. It was a time and dimension portal. Suddenly, McCoy jumped into that to go to the Earth's past.
Instantaneously, the Enterprise went out of existence. They concluded that McCoy changed something critical in the past which undid all Enterprise-level technological achievements of humanity.
Provided, Enterprise didn't exist, how did the search party exist on that planet? Without the Enterprise, they would never have been able to trek to the planet.
I am not concerned about McCoy's existence because it's a paradox. I am asking why the crew wasn't wiped from existence.