It's not uncommon for people to be in police custody for quite a while before receiving their "Miranda" rights. As you no doubt know, questioning people in custody, arrested or not, must be preceded by the administration of the suspect's Miranda rights. If the police fail to follow this rule, in most situations they cannot introduce the defendant's statements at trial.
(For more information on Miranda rights, see "Miranda Rights: What Happens If Police Don't 'Read Your Rights'." For more on the right to silence before the point of arrest, see Invoking Your Right to Remain Silent.)
But what about commenting on the defendant's silence, pre-Miranda and post-custody? For example, imagine a driver involved in a serious car accident, who is taken into police custody. Though the police do not question him, they note that he asks no questions about the well-being of the occupants of the other car. At the trial for vehicular manslaughter, the prosecutor must prove that the defendant was driving recklessly, and he uses the defendant's silence to support his theory ("He was so reckless that he didn't even care what might have happened to the people in the other car").
The first issue is whether the defendant was actually in custody. When it's a brief and routine traffic stop, the U.S. Supreme Court has held that such a stop doesn't constitute custody. Although most drivers would not feel free to leave, and the driver's freedom has been curtailed, the stop is open to the public and not "police dominated." Police can ask questions ("Have you had anything to drink tonight?") without first giving Miranda rights, and judges will allow the answers. (Berkemer v. McCarty (1984) 468 U.S. 420.)
The answer may be different, however, when the routine stop becomes prolonged, and particularly if scrutiny on the suspect increases. When a person is told he cannot leave, he could reasonably conclude that he's in police custody—triggering Miranda before any questions should be asked.
Defendants who can convince the judge that they were in custody and had not received Miranda rights will want to exclude from the prosecution's case in chief any evidence of their silence, as would the hypothetical driver above. (Using this silence to impeach a defendant who has testified is another question—see Can a prosecutor use post-arrest, pre-Miranda silence to "impeach" a defendant?) Interestingly, the U.S. Supreme Court has not ruled directly on the question, but several federal Circuit Courts of Appeal have faced it, with conflicting results.
One court that refused to allow such evidence pointed to the incentive a contrary rule would create for the police—to delay questioning in order to create an extended post-custody period, an intervening silence that could be used against the defendant. (United States v. Moore (D.C. Cir. 1997) 104 F.3d 377.) Another federal court pointed out that the Miranda rule was designed to safeguard the defendant's Fifth Amendment rights, and that the government should not be allowed to burden that right by implicitly pressuring the defendant to give it up and speak. (U.S. v. Velarde-Gomez (9th Cir. 2001) 269 F.3d 1023.)
But some courts have ruled otherwise. An example is a decision that emphasized the importance of knowing whether the defendant was under official compulsion to speak—only then, the court reasoned, would his silence be a "statement" for purposes of his Fifth Amendment rights. The court reasoned that, even though the defendant in question was under arrest and hadn't been read his Miranda rights, he wasn't being questioned and therefore wasn't under any compulsion to speak. So, the court said, evidence of his silence was admissible. (U.S. v. Frazier (8th Cir. 2005) 408 F.3d 1102.)
And as for that case involving the driver who didn't ask about the victims, the California Supreme Court sent the case back to a lower court. The lower court was to determine whether the defendant clearly invoked the privilege against self-incrimination. If he didn't, the evidence of his silence might have been properly admitted. (People v. Tom (2014) S202107); for more on the ruling, see Can the government use suspects' post-arrest, pre-Miranda silence against them?)