fulfillIfAnyRejected.js

function fetchDb(cancel) {
    return new Promise(function(resolve, reject) {
        if (cancel) {
            setTimeout(function() {
                reject();
                console.log('fetchDb cancel');
            }, 500);
        } else {
            setTimeout(function() {
                resolve();
                console.log('fetchDb done');
            }, 2000);
        }
    });
}

function fulfillIfAnyRejected(promises) {
    return Promise.race(promises.map(function(promise, index) {
            return promise.then(function() {
                return index;
            });
        }))
        .then(function(index) {
            promises.splice(index, 1);

            if (promises.length) {
                return fulfillIfAnyRejected(promises);
            }
        }, function() {
            return 'HAS_REJECTED';
        })
}


fulfillIfAnyRejected([
    fetchDb(),
    fetchDb(true),
    fetchDb()
]).then(function(res) {
    console.log('done', res);
});