The calls started last November. They often came late at night, when Melinda Sicari, an associate broker at Douglas Elliman, was about to go to bed or already asleep, and the callers were persistent. They’d either just sent money for an apartment to a Zelle or Venmo account or were about to send it. But something made them call the broker they thought they’d been communicating with. “They would say something like, ‘I just applied for your apartment and sent you the deposit.’ Or ‘I know this is going to sound really weird, but …’”