A Boston philanthropist has agreed to purchase the dilapidated, city-owned Modern Theatre and renovate it for use as a theatre and and commercial space. The former movie house has become so run-down in recent years that the city had to shut down a portion of the street it sits on and reinforce the structure to prevent cave-ins during winter snowfalls. The rebirth of the Modern is the latest in a series of initiatives designed to revive Boston’s theatre district, and provide a wider range of performance space for local groups.