(cw for suicide) Rory was saved when he and Amy decided to jump from a building together. Because a future, older version of Rory had already died that same night in the same building, this created a paradox where Rory died twice in one night. This time paradox killed the villains which were after them, the Weeping Angels, and both Amy and Rory woke up safe and alive in their own time.
In "Heaven Sent" and "Hell Bent," The Doctor tries to save his companion Clara Oswald from her death--a fixed moment in time, one that cannot be cheated by leaving a duplicate in her place, and which cannot be prevented without dooming the spacetime continuum. Despite this, The Doctor held out under 4 1/2 billion years of torture to hold onto information about The Hybrid, which is prophesied by the Time Lords to stand in Gallifrey's ruins and unravel the Web of Time, in hopes of having leverage to bargain for Clara's life. When he escapes, The Doctor takes over Gallifrey and pulls Clara out of the moment of her death with her biological processes suspended in a time loop. He attempts to take Clara far enough away in the hope that her pulse will resume and she will not have to be returned to the moment of her death, despite potentially damaging time itself in the process. When this fails, they go to the extreme end of the universe and find themselves in the ruins of Gallifrey. The Doctor reveals his intention to erase Clara's memories of him with a neural block taken from Gallifrey, hoping that the Time Lords will not be able to find her, but Clara insists on reversing the mental block on The Doctor instead, having accepted her death. They decide to do activate the mental block together, not knowing if Clara successfully reversed it, and The Doctor admits he became The Hybrid by trying to save Clara's life. The Doctor forgets Clara, and Clara sets off in a stolen TARDIS with the immortal Ashildr, taking the "long way around" to Gallifrey (where she will be sent back to her death).