Exactly how you do that (and I think it is a very, very poor idea - how do you get out of this loop?) will depend on the environment you are working in: a website will be completely different from a WinForms app for example.
But the principle is:
Handle the LostFocus event for the textbox.
In the event handler, create a new Textbox and add it to the page / form.
For WinForms:
void existingTextBox_LostFocus(object sender, EventArgs e)
{
TextBox existing = sender as TextBox;
if (existing != null)
{
TextBox newTextBox = new TextBox();
newTextBox.LostFocus += new EventHandler(existingTextBox_LostFocus);
newTextBox.Location = new Point(existing.Location.X, existing.Location.Y + 30);
newTextBox.Size = existing.Size;
Controls.Add(newTextBox);
}
}