During the last building boom, St. Vincent's Hospital Manhattan executives tried to pull out of financial trouble by making a deal with the Rudin Management Company, a prominent developer. Under the deal, Rudin was to buy most of the St. Vincent's campus for $300 million. It planned to renovate four hospital buildings and demolish four others and build luxury town homes and apartment buildings on their sites. Now St. Vincent's is closing, but officials are trying to preserve some medical operations, possibly an urgent-care center that could treat emergencies but would not admit patients. In a statement, William C. Rudin, chief executive of Rudin Management, said that he still wanted to develop the site and that a healthcare facility there would factor into his plans.