Is it possible to “steal” an event handler from one control and give it to another?

Yeah, it’s technically possible. Reflection is required because many of the members are private and internal. Start a new Windows Forms project and add two buttons. Then:

using System;
using System.ComponentModel;
using System.Windows.Forms;
using System.Reflection;

namespace WindowsFormsApplication1 {
  public partial class Form1 : Form {
    public Form1() {
      InitializeComponent();
      button1.Click += new EventHandler(button1_Click);
      // Get secret click event key
      FieldInfo eventClick = typeof(Control).GetField("EventClick", BindingFlags.NonPublic | BindingFlags.Static);
      object secret = eventClick.GetValue(null);
      // Retrieve the click event
      PropertyInfo eventsProp = typeof(Component).GetProperty("Events", BindingFlags.NonPublic | BindingFlags.Instance);
      EventHandlerList events = (EventHandlerList)eventsProp.GetValue(button1, null);
      Delegate click = events[secret];
      // Remove it from button1, add it to button2
      events.RemoveHandler(secret, click);
      events = (EventHandlerList)eventsProp.GetValue(button2, null);
      events.AddHandler(secret, click);
    }

    void button1_Click(object sender, EventArgs e) {
      MessageBox.Show("Yada");
    }
  }
}

If this convinces you that Microsoft tried really hard to prevent your from doing this, you understood the code.