<ListBox  SelectionMode="Multiple"  Name="MyListBox" >

 MyListBox.SelectedValue

    public class Person 
    {
        public string Name { set; get; }
        public int Age { set; get; }
        public bool IsSelected { set; get; }
        
    }

    public class MainModel : INotifyPropertyChanged
    {
        private ObservableCollection<Person> _persones;

        public ObservableCollection<Person> Persones
        {
            private set
            {
                if (Equals(value, _persones)) return;
                _persones = value;
                OnPropertyChanged();
            }
            get { return _persones; }
        }

        public ICommand LoadNewList { private set; get; }
        public MainModel()
        {
            Persones = new ObservableCollection<Person>();
            LoadNewList = new ActionCommand(OnLoadNewList);
            LoadList1();
        }

        private void OnLoadNewList(object obj)
        {
            LoadList2();
        }

        private void LoadList1()
        {
            Persones = new ObservableCollection<Person>
            {
                new Person {Name = "Roman", Age = 31 },
                new Person {Name = "Ivan", Age = 28 },
                new Person {Name = "Petr", Age = 34 },
                new Person {Name = "Nikolay", Age = 13 },
            };
        }

        private void LoadList2()
        {
            var oldList = Persones;
            var newlist = new ObservableCollection<Person>
            {
                new Person {Name = "Roman", Age = 31},
                new Person {Name = "Ivan", Age = 28},
                new Person {Name = "Petr", Age = 34},
                new Person {Name = "Nikolay", Age = 25},
                new Person {Name = "Vasiliy", Age = 65},
                new Person {Name = "Nikolay", Age = 54},
                new Person {Name = "Sofia", Age = 33},
                new Person {Name = "Olga", Age = 42},
            };
            var needSelect = newlist.Where(p => oldList.Any(z => z.Name == p.Name && z.IsSelected));
            foreach (var i in needSelect) i.IsSelected = true;
            Persones = newlist;

        }

        public event PropertyChangedEventHandler PropertyChanged;

        protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
        {
            PropertyChangedEventHandler handler = PropertyChanged;
            if (handler != null) handler(this, new PropertyChangedEventArgs(propertyName));
        }
    }

    public abstract class BaseCommand : ICommand
    {
        public abstract bool CanExecute(object parameter);

        public event EventHandler CanExecuteChanged
        {
            add { CommandManager.RequerySuggested += value; }
            remove { CommandManager.RequerySuggested -= value; }
        }

        public abstract void Execute(object parameter);
    }
    public class ActionCommand : BaseCommand
    {
        public ActionCommand(Action<object> action, Func<object, bool> condition)
        {
            Action = action;
            Condition = condition;
        }

        public ActionCommand(Action<object> action)
        {
            Action = action;
        }

        public Action<object> Action { set; get; }
        public Func<object, bool> Condition { set; get; }


        public override bool CanExecute(object parameter)
        {
            return Condition == null || Condition(parameter);
        }

        public override void Execute(object parameter)
        {
            if (Action != null) Action(parameter);
        }
    }

<Window x:Class="WpfApplication8.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:wpfApplication8="clr-namespace:WpfApplication8"
        Title="MainWindow" Height="350" Width="525"
        DataContext="{StaticResource MainModel}">
    <DockPanel>
        <StackPanel DockPanel.Dock="Top" Orientation="Horizontal">
            <Button Content="Load List 2" Command="{Binding LoadNewList}"
                    Padding="4" Margin="4"/>     
        </StackPanel>
        
        <ListBox ItemsSource="{Binding Persones}"
                 SelectionMode="Multiple"
                 Margin="4">
            <ListBox.ItemTemplate>
                <DataTemplate DataType="{x:Type wpfApplication8:Person}">
                    <TextBlock>
                        <TextBlock.Inlines>
                            <Run Text="{Binding Name}"/>
                            <Run Text=" - "/>
                            <Run Text="{Binding Age}"/>
                            <Run Text=" (IsSelected:"/><Run Text="{Binding IsSelected}" Foreground="Blue"/><Run Text=")"/>
                        </TextBlock.Inlines>
                    </TextBlock>
                </DataTemplate>
            </ListBox.ItemTemplate>
            <ListBox.ItemContainerStyle>
                <Style TargetType="{x:Type ListBoxItem}">
                    <Setter Property="IsSelected" Value="{Binding IsSelected}"/>
                </Style>
            </ListBox.ItemContainerStyle>
        </ListBox>
    </DockPanel>
</Window>

<Application x:Class="WpfApplication8.App"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:wpfApplication8="clr-namespace:WpfApplication8"
             StartupUri="MainWindow.xaml">
    <Application.Resources>
         <wpfApplication8:MainModel x:Key="MainModel"/>
    </Application.Resources>
</Application>