There are two good answers in this post: WPF listbox empty datatemplate
One of them that I tried with a little modification:
<Window x:Class="WpfApp1.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:local="clr-namespace:WpfApp1"
mc:Ignorable="d"
Title="MainWindow" Height="450" Width="800">
<Window.Resources>
<Style TargetType="ListBox" BasedOn="{StaticResource {x:Type ListBox}}">
<Style.Triggers>
<DataTrigger Binding="{Binding RelativeSource={x:Static RelativeSource.Self}, Path=Items.Count}" Value="0">
<Setter Property="Template">
<Setter.Value>
<ControlTemplate>
<TextBlock>No items to display</TextBlock>
</ControlTemplate>
</Setter.Value>
</Setter>
</DataTrigger>
</Style.Triggers>
</Style>
</Window.Resources>
<Grid>
</Grid>
</Window>