Let's say you (for some reason) cannot use a borderless WinForm, and you absolutely must use a console window. Well, you can kinda make it work.
Using most of the code from this similar problem over here, we can put together a solution that will work.
Here is an example borderless console window:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Runtime.InteropServices;
namespace ConsoleBorderTest
{
    class Program
    {
        [DllImport("USER32.DLL")]
        public static extern int SetWindowLong(IntPtr hWnd, int nIndex, int dwNewLong);
        [DllImport("user32.dll", EntryPoint = "FindWindow", SetLastError = true)]
        static extern IntPtr FindWindowByCaption(IntPtr ZeroOnly, string lpWindowName);
        [DllImport("user32.dll")]
        static extern bool DrawMenuBar(IntPtr hWnd);
        [DllImport("user32.dll", EntryPoint = "SetWindowPos")]
        public static extern IntPtr SetWindowPos(IntPtr hWnd, int hWndInsertAfter, int x, int Y, int cx, int cy, int wFlags);
        [DllImport("user32.dll", SetLastError = true)]
        static extern bool GetWindowRect(IntPtr hwnd, out RECT lpRect);
        [DllImport("user32", ExactSpelling = true, SetLastError = true)]
        internal static extern int MapWindowPoints(IntPtr hWndFrom, IntPtr hWndTo, [In, Out] ref RECT rect, [MarshalAs(UnmanagedType.U4)] int cPoints);
        [DllImport("user32.dll", CharSet = CharSet.Auto, ExactSpelling = true)]
        public static extern IntPtr GetDesktopWindow();
        [StructLayout(LayoutKind.Sequential)]
        public struct RECT
        {
            public int left, top, bottom, right;
        }
        private static readonly string WINDOW_NAME = "TestTitle";  //name of the window
        private const int GWL_STYLE = -16;              //hex constant for style changing
        private const int WS_BORDER = 0x00800000;       //window with border
        private const int WS_CAPTION = 0x00C00000;      //window with a title bar
        private const int WS_SYSMENU = 0x00080000;      //window with no borders etc.
        private const int WS_MINIMIZEBOX = 0x00020000;  //window with minimizebox
        static void makeBorderless()
        {
            // Get the handle of self
            IntPtr window = FindWindowByCaption(IntPtr.Zero, WINDOW_NAME);
            RECT rect;
            // Get the rectangle of self (Size)
            GetWindowRect(window, out rect);
            // Get the handle of the desktop
            IntPtr HWND_DESKTOP = GetDesktopWindow();
            // Attempt to get the location of self compared to desktop
            MapWindowPoints(HWND_DESKTOP, window, ref rect, 2);
            // update self
            SetWindowLong(window, GWL_STYLE, WS_SYSMENU);
            // rect.left rect.top should work but they're returning negative values for me. I probably messed up
            SetWindowPos(window, -2, 100, 75, rect.bottom, rect.right, 0x0040);
            DrawMenuBar(window);
        }
        static void Main(string[] args)
        {
            Console.Title = WINDOW_NAME;
            makeBorderless();
            Console.WriteLine("Can you see this?");
            Console.ReadLine();
        }
    }
}
This is pretty much a direct copy from the referenced link, here, and here. I tried getting the location of the form but I could not do it. I did manage to get the size, but the location was returning negative values for me. 
Although it's not great, it's a borderless console window. I really recommend just docking a textbox into a normal form. Here's a picture: "You need 10 reputation to post images"...