Простой способ, но не MVVM:
Xaml
<PasswordBox PasswordChanged="PasswordBox_PasswordChanged"
Xaml.cs
private void PasswordBox_PasswordChanged(object sender, RoutedEventArgs e)
{
if (viewModel != null && sender is PasswordBox)
viewModel.DatabasePassword = ((PasswordBox) sender).Password;
}
private void Load()
{
//Fills viewModel.DatabasePassword
viewModel.ReadData();
PasswordBox.Password = viewModel.DatabasePassword;
}