Right, I've just confirmed what I thought: we don't support "+", but parsing both "-0002-06-19" and "0002-06-19" work as expected. For the moment, if you need "+" support, I'd suggest adding a small amount of code to your application code to remove a leading "+" when parsing and add one when formatting - it's ugly, but hopefully just about good enough until Noda Time supports the "+" fully.
Note that the range of years supported by Noda Time is 9999 BCE (-9998 AN) to 9999 CE (+9999 AN).
Jon
using NodaTime.Text;
Test("-0002-06-19");
Test("0002-06-19");
// Fails
Test("+0002-06-19");
void Test(string text)
{
var pattern = LocalDatePattern.Iso;
var date = pattern.Parse(text).Value;
Console.WriteLine($"{text} => {date} => {pattern.Format(date)}");
}