> get the calendar data associated with these extreme time_points, using the code
The range of time points supported by the chrono library is typically a superset of the time points supported by the C library. These extreme time points would typically be well outside the range of time points that the C library can handle in a sane manner.
Since there is no "ctime_s" in C++, you'd have to say what library you're getting it from in case someone knows something about it that's not mentioned in its documentation.
Chances are, it produces an empty string where std::ctime would have resulted in undefined behavior, that is when the year requires more than 4 digits.
Also note that different libraries have different min and max for their system_lock:
With Clang's libc++ http://coliru.stacked-crooked.com/a/d46707a589e5aa58 I get
Sun Jan 10 04:00:54 294247
Sun Dec 21 19:59:06 -290308