Mosfets are 4-terminal devices with a gate that controls the conduction of the drain to source channel. The body (or substrate) of the typical n-channel enhancement mosfet is a P-type material with the drain and source formed from N-type materials.
The oxide layer insulates the metal gate connection from the other layers. There are holes in the oxide layer left for the metallic contacts of the drain and source.
N-P junctions act as diodes, and because the layers of the mosfet have P-type and N-type materials in close contact, diodes are formed from the body to the drain or source, as shown in the drawing here of the 4-terminal mosfet. If you were to leave the body connection floating, there could be no voltage flow through the two PN body diodes because they are reverse connected to each other.
However, in the 3-terminal mosfets (like the BS170) that are commonly used in guitar effects pedals, the body and source are connected internally and this shorts out the PN junction of the lower diode and removes it from the circuit. The top body diode can now conduct from drain to source because of the internal connection and therefore has to be taken into consideration during circuit design.
This means that every 3-terminal mosfet has a body diode due the construction of the device. It is not added as a separate component inside the mosfet.
However, there is something even more interesting in the 4-terminal mosfet. The drain-to-body-to-source structure is an N-P-N layered structure… NPN, as in transistor! There is a bipolar transistor in every mosfet!
Can you float the gate and use the drain-body-source as if they were collector-base-emitter? I don’t know but I plan on trying it. I would guess that it will probably be a poor bipolar but that may make it a special sounding unit (or an awful one). HFE will likely be low. It would probably be best to tie off the gate to keep it from acting as an antenna.
One last observation… I believe that the CD4007 has access to the substrate (body) and might be interesting for experimentation.