No, I don't think the hyphenated modifier "still-unresolved" is editorializing the situation in the following sentence that you presented:
"Asian shares drifted lower and the euro floundered near an 11-month low after the Federal Reserve failed to take any new steps to stimulate growth and offset the chilling effects of Europe's still-unresolved debt crisis."
What that modifier doing is only to indicate that there have been previous efforts to resolve that debt crisis but that it has persisted. It's actually a quick, more concise version of the phrase "Europe's debt crisis that remains unresolved," as in this longer sentence:
"Asian shares drifted lower and the euro floundered near an 11-month low after the Federal Reserve failed to take any new steps to stimulate growth and offset the chilling effects of Europe's debt crisis that remains unresolved."
Isn't it great that in English, hyphenating words in phrases can do that streamlining trick?