Added: I'm addressing a 3-wire feeder here, not paralleled conductors.
Under normal conditions, nothing. Think about old three-wire major appliances where the neutral was permitted to perform grounding functions (not the other way around). A sub-panel in a detached structure is another example, allowed only if there was no other effective ground/zero-volts reference available.
Allowing one conductor to act as both neutral and EGC risks energizing exposed conductive surfaces in case that conductor fails, as with open neutrals. Sub-panels, grounding terminals, and even plumbing could become energized relative to nearby conductive surfaces that are still at or near zero volts.
The purpose of an EGC is so an accidental contact between a hot conductor and a conductive surface mimics a hot-to-neutral fault, so the OCPD trips before someone is hurt. The EGC system begins at the last point where the neutral is allowed to be uninsulated. That point "defines" zero volts for the premises.