1. (one is) hiding from the police, the authorities, fleeing from the law
on the run
on the lam
on the loose
in hiding.
«Сегодня поздно вечером, гуляя в парке, я натолкнулся на какого-то человека, искавшего дорогу... Вид у него измученный, он, вероятно, несколько дней в бегах» (Федин 1). "Late this evening, while walking in the park, I came across a man trying to find his way...He looked exhausted, he has probably been on the run several days" (1a).
«Директор в бегах... как раз мы его ищем. Есть подозрение, что сбежал с казенным золотом» (Искандер 3). "The director's in hiding., we're looking for him right now He's suspected of absconding with government gold" (3a).
2. coll (one is) rushing around from place to place, incessantly running about taking care of business, doing chores etc
on the move (the run)
off (out) on errands
off (out) running errands
out and about
(in limited contexts) out running around.Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. С.И. Лубенская. 2004.