Rejected promises in Protractor/WebDriverJS

WebDriverJS and Protractor itself are entirely based on the concept of promises:

WebDriverJS (and thus, Protractor) APIs are entirely asynchronous. All functions return promises. WebDriverJS maintains a queue of pending promises, called the control flow, to keep execution organized.

And, according to the definition:

A promise is an object that represents a value, or the eventual computation of a value. Every promise starts in a pending state and may either be successfully resolved with a value or it may be rejected to designate an error.

The last part about the promise rejection is something I don't entirely understand and haven't dealt with in Protractor. A common pattern we've seen and written is using then() and providing a function for a successfully resolved promise:

element(by.css("#myid")).getAttribute("value").then(function (value) {
    // do smth with the value
});

The Question:

Is it possible that a promise returned by any of the Protractor/WebDriverJS functions would not be successfully resolved and would be rejected? Should we actually worry about it and handle it?