The concept of due process enjoys a long history. It's been around since before the United States began and is preserved as a core constitutional value in Texas and every other state. It is perhaps most associated with how the government is supposed to treat individuals suspected of criminal or civil wrongdoing to ensure quality of justice.
Despite the recognized value of promoting due process in the broad scope of matters, it was only in 1912 that it began to be applied to federal employment. That's when the first U.S. law took effect saying that workers could not be removed from a job without specific steps being followed for the protection of rights.