It's not typical heat-shrink tubing on the UEi design (121GW), it feels like silicone.
This simply cannot be a safety feature as it easily slides around, which actually makes it less safe if you're trying to hold the probe next to something dangerous. From my research, due to how this style of thermocouple works, you should not use it on anything that is electrically conductive anyway, since it can affect the readings (due to current flow). This style of sensor is a very low mass design, primarily to be used for measuring air (gas) temperatures, not direct contact with materials.
It also can't be anything you would use over the top of the thermocouple bead, because as an insulator it would impact the readings, or at least delay them greatly, which is the exact opposite of the entire purpose of this type of bead thermocouple design.
Is it to keep the braid from coming undone? Doubtful. While there are plenty of photos online showing an actual tight piece of heat-shrink instead, there are also lots of photos of these braided types without anything on the end at all. From my testing, I do not see it being necessary for this as the braid is just not going to come undone very much and also the silicone tube is constantly sliding around, even off the end, so it's a terrible solution to that anyway.
Personally, I think some good possibilities are it's an insulator for when you're holding it, or as protection for the wires if you have to clamp it in place.