Trade willingness is how highly they value what we offer them as our half of the trade, it's in the tooltip, not an actual willingness to trade with you.
ie, if you offer someone with 100% trade willingness 100 minerals it might give you 10 points in trade. If you offer 100 minerals to someone with 80% trade willingness they would give you 8. You then ask for things from them which will subtract from the points you got from your offer. If the net result is positive they'll accept the trade, if the net result is more than 1 an opinion modifier is applied equal to the points value of the trade (-1 IIRC) for giving them a good deal.
But fallen empires don't really care, so they don't get the opinion modifier. Because they're fallen empires.
EDIT: there are other hidden factors modifying how much they value what you offer btw, it's just that if there were two identical empires with identical planets, fleets, stockpiles, leaders, etc, etc, etc, but different trade modifiers they'd value your offer differently. And yes, I pulled those numbers out of my ass, no empire will value 100 minerals at 10 points ofc.