f.js

function f() { 
  throw new Error('def');
}

process.on('uncaughtException', function(e) {
  console.log('uncaught exception', e);
  f();
});

f();

g.js

function g() { 
  process.nextTick(function() { throw new Error('def'); });
}

process.on('uncaughtException', function(e) {
  console.log('uncaught exception', e);
  g();
});

g();

g.js.output

$ node index.js 
uncaught exception [Error: def]
uncaught exception [Error: def]
uncaught exception [Error: def]
uncaught exception [Error: def]
uncaught exception [Error: def]
... continues

j.js.output

$ node index.js 
uncaught exception [Error: def]