Bad Headphone Connector Wiring Issues - What Could Be Wrong?
What you describe could be explained with simply an open common, assuming that you channel to common short test is before the open, i. e. at the source.

With the open common, you have the phones in series with the ends connected between L and R. You are hearing the difference between the channels. This cancels out "centered" sound.

By shorting common to Left, at the source, you'd end up with the phones in series between Right and common. You'd hear only Right, being fed to both sides, though out of phase between sides.