The third wheel dilemma but worse

I know we’ve all encountered this social situation at some point but has anyone figured how to navigate it. Okay so say you are at work, a party, or conference or really any social situation where you do not know everyone. This thing will happen where I am talking to a Person I Know (co-worker, and another person, who I do not know but the person I was talking to knows, will jump in and start a conversation with the person I do know. Person I Know will either introduce me quickly or not at all because the conversation picks up quick. Suddenly, I’m the third wheel. Normally this would be fine as I know how to jump into a casual conversation. But in this case the two people start talking about something serious like their mom being in the hospital, someone else who is having a hard time, or some other top secret sounding work gossip or personal information. And I am just standing there. These conversations always go on too long where I am just standing not saying anything for minutes on end. I can’t jump into the conversation because it’s seems super personal and I don’t want to seem nosy. Do I just slowly back away? Do I just continue to stand there and wait until the subject changes? Maybe look at my phone so they don’t think I’m paying attention? I can’t change the subject because that would be very rude? Idk