A "sun-synchronous orbit" is typically a polar orbit that precesses so that it's sunside pass is always "over" the same local time (say, noon(ish)).
That puts it over the antipodean midnight time once it crosses the pole.
If you're thinking of a different orbit, how does that work?
> the dawn/dusk SSO orbit, where the local mean solar time of passage for equatorial latitudes is around sunrise or sunset, so that the satellite rides the terminator between day and night. Riding the terminator is useful for active radar satellites, as the satellites' solar panels can always see the Sun, without being shadowed by the Earth.
There are many SSO's for all the times of the day, most SSO's are not permantly in sunlight.
The comment I replied to implied that any old SSO would have the property of being always in the sunlight, this isn't true.
The particular issue with a terminator SSO is that region will get crowded (sure, space is large) and one collision will seed debris to spoil it for everyone for some time.
> Riding the terminator is useful for active radar satellites ..
All sats need some level of power or another, not all want to ride the terminator, see (for one example)
https://modis.gsfc.nasa.gov/about/
in which different sats in the constellation travel at different times of day (why?).