As I've said in the past, Butterfield and I have some friends in common and the story I got from one of these people is that once Farrell got fired the coaches were all told that there were no promises made regarding keeping the current coaching staff so if they got an offer from another team they may want to consider it. Over the next couple of months Butterfield got offers from four teams (Arizona, Florida, one I can't remember, and when the Cubs made an offer he accepted it.
I don't know what the timeline was regarding his signing with the Cubs as it pertains to signing Feebles but if Cora had been pro-active and wanted Butterfield it probably could have happened.