I'm going to jump off my own post and provide some real life examples so this is better understood.
LE has an active investigation. They have several people at the top of their list of possible suspects. They request an interview with the number one unnamed POI. They bring him in. They don't tell him he is not a suspect because at that point there are several unnamed suspects. They question him. They don't have to read him Miranda. They advise him that anything he says can be used against him in a court of law. He agrees to talk. He leaves out pertinent information in his statement, but they aren't ready to arrest or detain him. He is free to leave. He has become their unnamed suspect, but they don't necessarily "name" him a suspect because they want him to feel like they are stupid cops and he got one over on him. He is still a suspect. He just wasn't named a suspect. He doesn't have to be named a suspect. They can question 100 more suspects and come right back to the first guy and ask him to come in again for questioning. He agrees. LE knows he's their guy, but they don't have to tell him that...and they won't as long as he's talking. He starts to change his statement from the first version of events. It will be at THAT point that LE will likely read Miranda. If he wants to talk, he is free to continue to talk. If he doesn't ask for an attorney, he won't get one and everything he said is admissible in a court of law. He probably signed a statement acknowledging that when he was read Miranda. But at no point did LE ever tell this guy he was a suspect....even though he was a suspect from day one.