If you're looking for terseness, then these will do the job, in addition to what you have:

user.email = (email) ? email : user.email;

email && user.email = email;

(your linter will probably complain)

I myself would choose something similar to @ibowankenobi. I use TypeScript, so it's even easier since it will generate the necessary JavaScript for configuring properties:

export class User {
    private _email: string;
    get email() { return this._email; }
    set email(value: string) {
        if (value) {
            this._email = value;
        }
    }
}

const user = new User();
user.email = 'someone@email.com';
console.log(user.email) // someone@email.com
user.email = '';
console.log(user.email) // someone@email.com

With a mutation spell. Harry Potter has a few :)

A different take from ES6 , using a function and defaults applied.

let email = 'example@example.com';
checkEmail = ({userEmail = email})=>{
    return userEmail;
}

checkOtherEmail = (userEmail = email)=>{
    return userEmail;
}

checkEmail({userEmail = 'test@test.com'});
checkOtherEmail('test@test.com');

I guess there are different ways to do that, and all of them are valid. I prefer to use an if-statement:

if (email) {
   user.email = email;
}

You could also use a setter (which you might even make very generic, so you could assign it to any object):

const user = {
  email: undefined,
  getEmail: () => this.email,
  setEmail: email => { this.email = email || this.email; },
  unsetEmail: () => { this.email = undefined; },
};

user.setEmail(email);

If you want to be extra careful (since above solutions might be dangerous in certain situations):

if (typeof email !== 'undefined') {
   user.email = email;
}

// alternatively, using roption-js or similar,
// which adds Rust inspired Options

if (email.isSome()) {
  user.email = email.unwrap();
}

function createUser(){
    this._email = undefined;
};
Object.defineProperty(
    createUser.prototype,
    "email",
    {
        configurable:false,
        enumerable:false,
        get:function(){
            return this._email;
        },
        set:function(v){
            if (!this._email) {
                this._email = v;
            } else {
                console.log("Email has been set already!!");
            }
        }
    }
)

Then:

var user = new createUser();
user.email; //undefined
user.email = "some@email.com";
user.email; //"some@email.com";
user.email = "some2@email.com"; //"Email has been set already!!"
user.email; //"some@email.com";

I wrote a plain old style js, so that others can use it ie9+. Do your custom sanitization etc inside the set handler (also make the own _email property a getter/setter that works with a salt enclosed in an iife, so no other can set them). There are many many other ways to achieve similar stuff, this is one of them.