From Longman Dictionary of Contemporary Englishbe running scaredbe running scaredWORRIEDto feel worried because someone who you are competing against is becoming very successful or powerful The party are running scared. → run
Examples from the Corpus
be running scared• Their new software has the competition running scared.• Then why is it that Chretien appears to be running scared?• To me, ti just looks like the fools are running scared.• Whenever managers were laid off, he sensed in the ranks ever-higher levels of anxiety Even those who remained were running scared. 