Conversations with the police can yield more than confessions. Sometimes they lead to physical evidence.
What happens when the police elicit incriminating statements after violating a suspect's Miranda rights? The statements will likely be inadmissible in court—this much we know. But what about the additional evidence the statements lead to? Is that evidence admissible, or is it "fruit of the poisonous tree"?
In a 2004 case, United States v. Patane, the U.S. Supreme Court established that the "physical fruits" of statements coming after Miranda violations are typically admissible. If the police are supposed to—but don't—provide the Miranda warnings, and the suspect says something that leads them to physical evidence, that evidence normally doesn't have to be suppressed. (542 U.S. 630 (2004).)
In Patane, an officer was investigating whether the defendant, a convicted felon, violated a restraining order. The officer received a tip that the defendant had a gun (illegally). The police arrested the defendant at his home for violating the restraining order. One of the officers began to give the Miranda advisement, but the defendant interrupted to say that he knew his rights. The police asked him about the gun; he divulged its location, and the officers went and got it.
The prosecution acknowledged that the defendant's statements were inadmissible because the police didn't finish the Miranda warnings. But it argued—and the Supreme Court agreed—that the gun was admissible.
The decision created the following rule:
Physical evidence that comes directly from a confession won't be excluded just because there was no Miranda warning. But, if the police not only failed to Mirandize, but also coerced the statement out of the suspect, then the evidence will probably be suppressed.
Remember: The police don't have to give the Miranda warning every time they arrest someone or ask someone questions. It's possible for a suspect to give an incriminating statement without Miranda applying at all. Of course, in that kind of situation, both the statement and any evidence it leads to may well be admissible in court.
On the other hand, you should know that the law in any given state can protect defendants more than a U.S. Supreme Court ruling does. For example, a state court could interpret the state constitution to mean that Miranda violations invalidate the statements and the evidence they produce.