A Lubavitch chasid's talis gadol has a special way of being tied that ensures that the tzitzis hangs off of the side of the talis and not off of its front or back.
In his Piskei Siddur, the Baal HaTanya writes that the hole the strings come out of should be more than the width of thumb from the corner of the garment. This is learned out from the fact that it says the strings should be "Al Kanfei" (On the corners) and not "In the corner".
The Baal HaTanya learns out from the verse (Devarim 22:12) "גְּדִלִים, תַּעֲשֶׂה-לָּךְ, עַל-אַרְבַּע כַּנְפוֹת כְּסוּתְךָ" that from the hole until the first knot is not considered part of the strings (Gedilim), which is why it is not counted when measuring the length of the strings.
Therefore, even the first knot should be a little more than a thumb's width from the corner of the Tallit Gadol.
When softer material started being used to make the Garments (as displayed in the picture in the question), it was possible for the strings to slip down, causing the first knot to get closer than the minimal thumbwidth's requirement. So that people wouldn't constantly have to check the position of the first knot during prayer, the Baal Hatanya said to add a small hole and thread the largest string through it, after making the first knot. This would prevent the knot from slipping down.
[The Baal HaTanya also holds that the hanging strings should touch the corners, which is why the knot is tied on the side and not the bottom, see here. However, this is not the reason for the little hole (it is why the hole is placed where it is, but it is a separate thing).
See here where Rabbi Levin (editor-in-chief of the new print of the Shulchan Aruch HaRav) makes this clear]
This is not necessary on a Lubavitcher's Tallit Katan, since the strings are threaded through a double hole, and the first knot is tied right there. There is therefore no problem with ensuring that there is a minimal thumbwidth's (and a little extra) space from the knot to the corner. See here for illustrations.