private string _data;
public ObservableCollection<string> Data
{
        get { return _data; }
        set { _data = value; OnPropertyChanged(); }
}

<CheckBox Content="галка" IsChecked="{Binding Model.IsSplit}">
    <CheckBox.Style>
        <Style TargetType="CheckBox">
            <Setter Property="Background" Value="Black"/>
            <Style.Triggers>
                <DataTrigger Binding="{Binding Model.Data, Converter={StaticResource nullOrEmptyToBoolConverter}}" Value="False">
                    <Setter Property="Background" Value="Red"/>
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </CheckBox.Style>
</CheckBox>