Dont think that we have addressed the problem here folks!
Firstly go get one nail that just fits nicely inside the collet and tube of the pencil and cut it on hacksaw/grinder or bite the end off so that it is now 98mm long.
The problem with the collet end falling off is that it was never put on (properly). Without the nail you stand a damn good chance of cocking up every other kit as the collet needs to be pressed onto the tube against the presure of the spring and it needs three hands and the patience of a saint.
Get the nail and thread the components on like this:
Push them up so they look like this:
Now carefully compress thespring so that you feel the collet slip inside the long thin easily breakable tube on the right hand side of the picture (get the problem! easy to compress and bugger up the tube if you dont have it aligned properly!)
Once you feel that the collet is inside the tube, compress the assembly between the nail head and the end of the flimsy tube and you will feel the collet slip inside the flimsy tube. .
Continue with assembly