For context I'm in engineering consultancy, so by no means an expert but I probably have enough experience to be on the other side of the Kruger curve dip.
Passive sonar in the naval sense means listening only, not emitting. Do you mean imaging that relies solely on acoustic energy already present and emitted by the body? If so, then generally no. You have two types of "passive" imaging. First would be hardware-passive, as in MR elastography (most common), where the patient wears a transducer pad, and vibration is actively generated by a driver. You've then got algorithmically-passive, which is more analogue to passive sonar, reconstructing tissue stiffness from ambient broadband vibration without the emitted probing pulse, but that is very much entirely academic. I guess the question would be, why is it worth pursuing when you have something like optical coherence elastography (OCE) for non-invasive profiling. Doing it using noisy ultrasound method becomes redundant. There are other methods, but the outcome is the same.
Generally (this is true for all systems, not just humans) you need to induce energy into it to more effectively measure it's output. Think of it like a bell - if I want to hear the note it produces, it's much easier to hear what this is if I ring it with a hammer. Granted, it will be "passively" resonating to a point where, with a sensitive enough sensor, I could probably pick up the output without the hammer - but that is a pointless problem to solve. I could hit a bell with a soft hammer a million times over without causing damage to it. The lifetime of the person hitting it with a hammer is far shorter than the accumulative damage to the bell before it breaks. The same is true for humans. You could effectively run a very low-energy, 60Hz vibration through a person (which is how the pads work) for multiple lifetimes before it would cause significant damage, so there comes little point in solving that problem. As such, true "passive" imaging is functionally pointless if your outcome is "safely image a patient". You're overengineering your solution to solve a problem that is only relevant if your patient was planning on living for 1000+ years.