any signal needs two terminals to be injected in any circuit. Some way or another an earth will be introduced to the circuit. Are you asking about (Power Line Communication - PLC)?
Electromagnetism conserves electric charge. So if you send any electric signal into and along an electric conductor, it must return to the source. Otherwise you could define a volume integral around the single-conductor inlet, where you dump charge that would seem to disappear. This argument holds for high-frequency signals as well. The only way to use a single conductor would be a wave guide, where on the inside you excite a transversely polarized wave, which travels along the tunnel with its well-defined boundary conditions at the walls.
If we can illustrate our need on the following image,We think Saad and I that your proposal to use electric wave is intresent in playing on the frequency to pass information to the receiver in addition to the power supply,
as the function of Axon (nerve fibers ) that typically conducts electrical impulses away from the neuron's cell body
So we can use a single electric conductor without using another one to go back to the source
It is possible provided there isn't any DC component in your signal. Beside wave guides you could use transmission lines (single wire lines or Goubau lines). However with transmission lines, both at the sender as well as at the receiver you need an additional element with sufficient capacitance (another line, a sufficiently large piece of metal, etc.) in order to provide or receive the charge moved by the sender / moved through the receiver into or away from the line.
I don't think an axon is a valid example because there are electrochemical / physiological processes involved; and the propagation mechanism of axons includes a current through the inside as well as through the medium at the outside of the axon, so one could argue that this is a two-conductor-propagation resp. that the surrounding of the axon serves as some kind of "ground".
in Glenn S. Smith's book "Classical electromagnetic radiation" part of chapter 8 is dedicated to the radiation resp. non-radiation of traveling waves on thin wires. Although the present question does not concern PLC, signals on single overhead power lines are virtually independent of the low frequency power transmission. I seem to remember a recent article containing a picture of a kind of cone with a gap which can be slipped onto a single wire and is used to couple the signal to and to pick it up from the wire.
Something similar but from 1983 is: Indulgar et al.: Some Studies On Carrier Propagation In Overhead Transmission Lines
An article on Goubau lines including some references here on RG: