If they do exist, what is advantage of using them? How often are they used in comparison with mosfets that have integrated diode?
It's possible to manufacture 4-lead MOSFETs with the body connection (aka "back gate") brought out, but I think they are pretty rare.
You'll see parts with the body not tied to source used in chips, for example to make a good transmission gate.
In the above, when the body is tied to Vcc the diode junction does not become forward biased until the voltage exceeds Vcc, allowing the TG to pass signals over the whole GND to Vcc range.