Unicode 6.1 mentions that U+1EEF0 and U+1EEF1 are used for Arabic sum
and Persian limit. Additionally, Azzeddine Lazrek indicated to me that
U+1EEF1 is also used for Arabic product.
https://www.w3.org/TR/arabic-math/ also mentions a special stretched
character for Arabic limit, but it does not seem to have been included
in Unicode at the end.
Regarding the default value, I think the "prefix" and "stretchy"
properties added by David are correct. I don't know about the spacing,
but the default thickmathspace value is probably too big. So in the
doubt, I'd recommend setting the default lspace/rspace to 0 or 1.