Are saying the outer wire stretches out after the clapton wire is finished being twisted up? As in, while you're wrapping the coil?
That's a pretty easy fix.
Start twisting it in the drill as normal. Just get it into the groove and do a quarter-inch of normal clapton. Make sure those wraps are the tightest they can be and guide the wire back over itself to make a little 1/16" bundle. Just a little lump will do. Bring it back into the groove and clapton like you normally would right up until you only have at least a quarter inch (half may make it easier) of bare wire left. Again, bring the wire back over itself to make another little bundle.
Don't stop after making the bundle. Do like you did before and clapton the little bit of bare wire left. It just helps secure the wire that much more.
The knots on the ends work because they keep tension on the wire. It usually expands slightly when you remove it from the drill or cut it, which makes the diameter increase and thus brings the sliding. The knots keep the outer wire compressed enough to grip the core nice n' snug.
This has only failed me a few times. The wraps literally have to be as tight as possible to stay in place, but if your technique is on point, it will work well enough.
I use a different method. When I'm setting up, I bend the the first 1/4" end going into the chuck to a 90 degree angle. Doesn't have to be a perfect angle... ...it only needs to be an abrupt bend. I start wrapping 4-6 inches of the outer wire 1/8" in front of the bend, going back towards and over the bend. From there I just go back and forth over the little 1/4" piece and the rest of the core. I'm sure most people do something similar but for this technique, it is particularly important.
With everything in place, I go right into making a clapton the normal way. When I get to the end of the core wire, I don't stop or double back - I just pinch the the end of the core and crank the drill until the outer wire snaps off all on its own. This weakly fuses it to the end and keeps it from winding back during the next part.
With the finished wire still in the chuck, I tightly bend the last 1/8" over itself with my fingers. To lock it in, I just crimp it tight with pliers. You want a straight crimp. The end piece and the rest of the wire should be parallel to one another
After that, its fine to remove the wire from the chuck. The crisscross wrapping on the section in the chuck keeps it from rebounding. You can keep it that way and wrap your coil, but I crimp that end and snip the excess. Sometimes that end doesn't stay perfectly secure if I don't.