Improving MVC 4 DropDownList
Can I access both RoleName and ID without fetching it in the backend?


Yes, I believe so if you want to write a bit of javascript.  You would need to create a 
hidden field and on every select list change event set the value of that field.

Something like

$(body).on("change", "#selectbox", function() {
    $("#inputbox").val($(this).val());
});


I'm also unsure as to why you are creating the database connection twice but I would consider
passing that into the GetRoles method like so:

public  IEnumerable&lt;NewLogin&gt; GetRolesForDDL(database db)
{
    return (from r in db.UserRole
            select new NewLogin
            {
                UserRole = r.Role,
                RoleID = r.RoleID
            });     
}    
public  NewLogin RoleDDL()
{
    using (database db = new database())
    {                               
        var roles = GetRolesForDDL(db).ToList();
        // populates ddl
        return new NewLogin
        {
            RoleList = new SelectList(roles, "RoleID", "UserRole");                
        }
    }
}


Or even if both of these methods are part of a class consider passing the database into the class constructor and using it as a private instance variable.