Final answer:
The right of Habeas Corpus can be suspended in the United States under the Constitution only during times of Rebellion or Invasion when public safety is at risk, as evidenced by historical precedents during the Civil War both in the Union and the Confederacy.
Step-by-step explanation:
The right of Habeas Corpus, a fundamental legal protection against arbitrary detention, can only be suspended in specific and dire situations. The United States Constitution stipulates that the Privilege of the Writ of Habeas Corpus shall not be suspended, unless in cases of Rebellion or Invasion when the public safety may require it. This was enacted during the Civil War, when President Lincoln suspended the writ to ensure Union security and detain suspected Confederate operatives.
The Lincoln administration also took measures such as shutting down newspapers to maintain national security. Similarly, during the Confederacy, Jefferson Davis was granted the power to suspend habeas corpus, leading to significant civil liberties controversies.