Let's say that George is a quiet, middle-aged store-clerk with a marriage of 23 years. He's always been faithful to his wife, whom he loves. For a hobby he restores antique furniture.
The unexpected is if George falls in love with the boy next door. The unthinkable is if he ties his wife up in the tool-shed and slowly eats her alive.
The unexpected is a staple of fiction. Unpexpected twists of plot or character maintain reader interest. Selling the unexpected is a matter of providing the right stimulus/response... We might learn how George hates how he's growing old... how he yearns for his youth, how he almost had a gay affair in his teens, and how his middle age is rekindling that... That's the unexpected.
The unthinkable is a much harder sell. George is stable and loves his wife. Why would he possibly do something so callous, cruel and destructive as eat her alive? Stimulus/response is not enough to sell the unthinkable. We need to make a compelling, passionate argument as to why this action is the only one George can take.
The unexpected surprises us. The unthinkable typically shocks and sometimes horrifies us. The unexpected keeps us reading. The unthinkable sometimes makes a novel unforgettable.
So, when do you have a character do the unthinkable? Why? When would you rather not have the unthinkable in your story? Why not? At what point in your writing do you decide: I need to introduce the unthinkable here? And how do you decide what sort of unthinkable thing to introduce?