[wideawake]

"The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it."

Since it is the responsibility of the executive to provide a writ of habeas corpus, the suspension of the writ would entail the executive not providing it - but not providing it only in the circumstances above described.

[Squawk 8888]

Habeas Corpus writs are issued by the courts, not the executive. Any citizen in custody has the right to apply for one in court.