From Longman Dictionary of Contemporary Englishcome runningcome runninga) informalOBEY to react in a very eager way when someone asks or tells you to do something He thinks he’s only got to look at me and I’ll come running. b) especially spokenSYMPATHIZE to ask someone for help, advice, or sympathy when you have a problemcome running to Well I warned you, so don’t come running to me when it all goes wrong! → run
Examples from the Corpus
run to• But even so, why had he not come running to find out what was happening?• At once there came running to her from all directions a pack of great wolves.• I had to stay there without moving a finger, until Glumdalclitch came running to rescue me.• When children came running to them for sweets, they scythed them down with automatic fire.• It was wrong of me to come running to you. 