Paramedic and former ambulance service director here: In my jurisdiction the car is the sole responsibility of the police - in theory. So basically we call the police and let them handle it. They will decide if it’s safe to leave it where it is (e.g. if it’s on a highway, post accident or otherwise a traffic hazard). They will usually ask the patient if they should call a specific company or,if the car is still roadworthy, if they should call someone like a relative to get it - within certain limits of course, they won’t do that on a highway and if the relative is two hours away the patient is also SOL.

If the car is stationary as in a safe and legal parking spot it’s a bit different, then in theory we could still call the cops,but they would hate us for it when the patient is conscious. In these cases most crews simply lock down the car and give the key to the patient - the same way we lock down an apartment when we leave with a patient.

The only case when we might leave a car unlocked and unattended is an unresponsive patient that has a transport priority,aka we need to go NOW. We will still call the cops (and they will either find a way to secure the car or tow it),but we sure as hell won’t wait. While I might have a minute to spare waiting for the cops for an average unconscious patient e.g. post seizure there are a lot of reasons where I don’t have that - and might not have the time in some awake cases as well. In these cases a car might be left unlocked - especially in times when the key rarely is still required in the ignition anymore where I can easily find it. But in these cases the life of the patient takes priority over any material assets.

(To give you a more practical example: The last guy I left the car unlocked was a gentleman with sudden onset of massive pain between the shoulder blades and a large difference in blood pressure values between the arms - a good sign of a thoracic aortic aneurysm, a very deadly condition. That’s a “fuckfuckfuck we need to go now” condition. I looked for the car key once for around 5 seconds,the car was a mess, I couldn’t find it. Dispatch sends the cops,but they often take a long time here once they know we are no longer on scene. Sadly he didn’t even make it to the hospital alive. But we tried).