Donald Davidson's Swampman example is typically used to make this point vivid: You visit a swamp. Lightning strikes, killing you. Simultaneously, through incredibly-low-odds freak quantum chance, a being who is molecule-for-molecule identical to you emerges from the swamp. Does this randomly-congealed Swampman, who lacks any learning history or evolutionary history, experience pain when it stubs its toe? Many people seem to have the hunch or intuition, that yes, it would; but any externalist who thinks that consciousness requires a history will have to say no. Dretske makes clear in his 1995 book that he is quite willing to accept this consequence. Swampman feels no pain.
But Swampman cases are only the start of it! If pain depends, for example, on what is normal for your species, then one ought to be able to relieve a headache by altering your conspecifics -- for example, by killing enough of them to change what is "normal" for your species: anaesthesia by genocide. And in general, any view that denies local supervenience while allowing the presence or absence of pain to depend on other currently ongoing events (rather than only on events in the past) should allow that there will be conditions under which one can end one's own pain by changing other people even without any changes in one's own locally-defined material configuration.
To explore this issue further, I invented a tyrant with the headache, who will do anything to other people to end his headache, without changing any of his own relevant internally-defined brain states.
"The Tyrant's Headache" is a hybrid between a science fiction story and an extended philosophical thought experiment. It has just come out in Sci Phi Journal -- a new journal that publishes both science fiction stories and philosophical essays about science fiction. The story/essay is behind a paywall for now ($3.99 at Amazon or Castalia House). But consider buying! Your $3.99 will support a very cool new journal, and it will get you, in addition to my chronicle of the Tyrant's efforts to end his headache (also featuring David K. Lewis in magician's robes), three philosophical essays about science fiction, eight science fiction stories that explore other philosophical themes, part of a continuing serial, and a review. $3.99 well spent, I hope, and dedicated to strengthening the bridge between science fiction and philosophy.