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Basic Trope: Someone turns back time in an effort to change the past, but realizes that the past cannot be changed, or might have even been caused by himself/herself.
Straight: Alice fell off the building to her death. Bob looked up the moment she landed to find her killer, and saw a figure disappearing into the building. Bob turns back time in an effort to save Alice and find the culprit, and runs to the top of the building where Alice fell off from, but the moment he yells for her, she was so shocked she fell off to her death. Bob realizes that the reason why Alice fell off was because he turned back time to save her, and that the figure that he's seen in the building back then was actually himself.
Alice traveled into the future only to see her own gravestone and hearing about how a mysterious stalker caused her untimely death. She becomes paranoid to the point of never leaving her building. One day, she decided that it would be safer for her to scout the surrounding area for the killer that is inevitably coming her way. People notice this and suspect that she wants to commit suicide by jumping off from the top. Alice starts to suspect everybody to be the killer and refuses to get help, because the person she would confess her fears to might be or attract the murderer. Even worse, her words might inspire some sick deviant to commit the crime. Standing on the rooftop, she contemplates the inevitable. Suddenly she hears footsteps and a loud scream behind her, which scare her enough to lose balance and fall into her death.
Filled with remorse, Bob travels further back in time in order to prevent the building from which Alice fell into her death from ever being built. While attempting to sabotage the construction project, he is captured by a mysterious masked character. After returning Bob to the present, the figure explains why he had to be stopped. It turns out, that Bob's parents where involved in the construction of the building. By getting the job there, they couldn't go to the annual city festival that year, when the mass-shootings took place. They met each other at work and fell in love. Bob understands that even if he saved Alice, he would have destroyed the life of countless people in the process, which wouldn't be much of aHeroic Sacrifice.
Justified: The rules of time travel specifically work this way, as is eventually explained to Bob.
Inverted: Bob successfully changes the past. This creates an alternate timeline, in which Bob goes back in time again and changes something else, creating yet another timeline, and so on.
Subverted: Years later following the incident, despite being told that nobody can change their fate, Bob becomes the leader of a secret Time Police. They get a warning message about a terrorist they need to stop somewhere in the past, otherwise the city will cause a global economic collapse and destruction of thousands of lives. Bob leads his squad of highly skilled professionals to infiltrate the past without being noticed by the public. When they split up, the leader notices the attacker and quickly subdues him, saving the day.
Double Subverted: Bob recognizes the terrorist - it was Bob, who attempted to stop a construction project, so that the building existing in his present day won't be there for Alice to fall from. The secrecy of the operation also is blown and Bob makes a huge Face Palm when he remembers those strange "cosplayers" from the newspaper he read with his dad when he was a kid. Faced with the evidence, the Time Police closes down indefinitely.