When a government convicts someone to death without holding a trial first, it's done with a law known as a bill of attainder. This kind of legislation is not allowed under the rules of the US Constitution.
Historically, the word attainder has meant "giving up land and civil rights as a consequence of a death sentence." In a bill of attainder, legislators have enacted a law imposing this sentence, rather than going through the process of an actual trial. In 1542, King Henry VIII had several prisoners executed using bills of attainder. Modern governments are critical of this method, and it's explicitly banned in the US Constitution.