For example, therapist may be split into the + rapist, neither of which (arguably) has anything to do with the original words.
Another example would be conflagration: con + flag + ration. Or weather: we + at + her.
Note that words like threesome and purebred would not qualify, because the parts are intentional and contribute to the original word's meaning.
It seems to me there might be a word for this, which I would describe as "accidental lexical componentry" — but I'm not sure there is one. And if I do think of one I will be sure to add a supplemental (supple + mental) section (sect + ion) to this question (quest + ion).
Best Answer
They are called redividers or redivided words:
They are apparently also known as charades. Quoting from The Dictionary of Wordplay by Dave Morice:
There are a number of domain names which have become infamous thanks to their ... redivisibility: