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Basic Trope: Something offhandedly mentioned or seen early on is important later.
Straight: During his first interaction with Alice, Bob casually mentions his grandmother has cancer. Later on, Bob's grandmother dies, so he has to go to her funeral and can't help Alice.
Exaggerated: Everything Bob says in his first conversation with Alice adds up to a number of reasons for why he can't help.
Downplayed: Bob mentions that his grandmother has cancer. Not too long later, she dies, putting him in a temporary Heroic BSOD that he quickly snaps out of. His grandmother and all related events are never mentioned again.
Justified: Bob's a nice guy and would want to be at his grandmother's funeral. Wouldn't you?
For whatever reason, Bob says his grandmother doesn't have cancer. Later on, he can't help Alice because his grandmother is okay.
Or Bob's grandmother has cancer and dies. Alice visits her funeral instead and can't help Bob.
Or Bob's grandmother has cancer, but it's Bob that dies instead.
Or Bob's grandmother dies from cancer early in the story, then Bob tells Alice about it much later.