Didn't the ancient grave-robbers who looted the pyramids do exactly that?
I don’t think that they ever caused the kind of damage that would have revealed the inner construction. They stuck to the chambers where the treasure was.
There’s a diagram in this topic, borrowed from an older topic, showing the three known examples of tunnels burrowed through the structure (the access holes leading to the relieving chambers above the King’s Chamber; the Well or Robber’s Hole leading from the Ascending Passage to the Descending Passage; and the Mamun passage that was cut in for one of the caliphs). Not one of these encountered any rubble pile.