That little tube can withstand high temperatures and it’s on the thermister and keeps the 2 wires from shorting out. The thermister is the device that tells the board how hot the heater block is.
The wires are crimped together as solder would melt. So you need to find a crimp connector and hook both wires back up properly. If this is not done properly your printer will show the wrong temperature and could overheat and even catch fire. If you are not familiar with doing this you need to find a friend to do it or maybe contact Lulzbot and see if they will sell you one with the wires connected already.
The small solid wires on the thermister do not like being bent and they will snap if too much bending is done and this is likely what happened to yours.
Oh, and the thermisted is just shoved into that hole, you will likely be best to remove it and undo the plug on the other end so you can lay it out to fix it.
This is what is inside the hole https://www.lulzbot.com/products/100k-epcos-thermistor