It seems unlikely that there is such a word. Many idioms stem from an actual, non-idiomatic usage so it doesn't seem surprising that there are idioms that can still function in a non-idiomatic form.
- He let the cat out of the bag by letting the cat out of the bag.
- If you scratch my back by scratching my back, I'll scratch your back by scratching your back.
- The airplane ran out of runway by running out of runway
Such an idiom is one that can function as both "literal" and "figurative":
literal — taking words in their usual or most basic sense without metaphor or allegory
figurative — departing from a literal use of words; metaphorical
The act would be a literal action that also satisfies the figurative meaning of the idiom. Placing them both in the same sentence is just wordplay -- I wouldn't even count it as a self-referential usage. It is more akin to a tautology:
tautology — the saying of the same thing twice in different words, generally considered to be a fault of style (e.g., they arrived one after the other in succession)
With the exception that you say the same thing twice, with the same words but switching between literal and figurative use. Does a word describe such double-usage? I don't know of one, no.