unknowFriend.js

let users = [{
    name: 'John Foo',
    email: 'johnfoo@test.com'
},
{
    name: 'Ary Blee',
    email: 'aryblee@test.com'
},
{
    name: 'Aston Martin',
    email: 'astommartin@test.com'
},
{
    name: 'Lorem Ipsum',
    email: 'loremipsum@test.com'
}];
let sortedUsers = [];
function sortNext(users, sortedUsers) {
    let owner = {};
    let randomIndex = null;
    if(sortedUsers.length === 0) {
        randomIndex = Math.floor((Math.random() * users.length));
        owner = users.splice(randomIndex, 1)[0];
    } else {
        owner = sortedUsers[sortedUsers.length - 1].sorted;
    }
    randomIndex = Math.floor((Math.random() * users.length));
    var sorted = users.splice(randomIndex, 1)[0];
    sortedUsers.push({ 
        owner: owner,
        sorted: sorted
    })
    if(users.length === 0) {
        sortedUsers.push({ 
            owner: sorted,
            sorted: sortedUsers[0].owner
        });
        return false;
    }
    sortNext(users, sortedUsers);
};
sortNext(users, sortedUsers);
console.log(sortedUsers);