starve out of some place
starve (one) out of (something or some place)
To deprive one of food in order to force one to exit or flee some place. Rather than risking their officers in a gun fight, the police decided to simply starve the criminals out of the building in which they had barricaded themselves. The empire's army began starving the rebels out of the contested city with a siege that lasted nearly three months.
starve (someone or an animal) out of some placeand starve someone or an animal out
to force a living creature to come out of a hiding place or a place of security by starvation. The attackers tried to starve the people out of the walled city. We tried to starve out the mice.