Do HIV particles die without host cells?
I've learnt that our circulatory system can clear foreign matters from blood stream. Phagocytes can engulf and breakdown virions. Our liver and spleen is the blood filter system, which sequesters foreign matters all the time. So free floating HIV virions can't stay indefinitely in our blood stream.

However, without an effective adaptive immune response, these mechanisms are still unable to suppress viral replication. That's why HIV patients still have high viral load if untreated.