Longman Dictionary of Contemporary English - besiege

~ v 1 to surround a city or castle with military force until the people inside let you take control  (In April 655, Osman's palace in Medina was besieged by rebels.) 2 usually passive if people, worries, thoughts etc, besiege you, you are surrounded by them  (Miller was besieged by reporters and press photographers.) 3 be besieged with letters/demands/requests etc to receive a very large number of letters, requests etc