When a person is extremely distraut, confused, beaten or just generally pissed at a person or event. Or has a face to face run in with the cops or Chuck Norris.
You say this word as a curse when you start to say the word 'shit', but mid word something happens that makes 'fuck' the more applicable of the two words so you finish your started 'sh-' with a 'fuck', thus resulting in 'shfuck'.
There's a cop behinds us, oh shfuck! He's pulling us over.