Bad things happen. Threads break.
It's especially annoying when they break during sectional beaming, because I don't always notice right away. This is what happened here. I'd wound on several turns before I twigged a thread had broken. :(
What I do in this instance is re-thread the offending end through the tension box, loosely coil about a yard and a half or so, tuck it into the warp and continue beaming.
When the broken end surfaces, I pull the coil out, tie it onto a repair end and hang it off the back of the loom.
The repair end goes from the bottom and up the centre of the cone. The cone is then run under the tension box rail, and over the rod in the ceiling that doubles as my warping valet.
It is but a matter of a moment to grab the loop at the butt of the cone and pull off a yard or so and then let the cone down to about an inch or so off the floor.
As I weave, the cone automatically rises. When it gets to within 6 or so inches of the bar in the ceiling, I go round to the back of the loom, yard off some more yarn and drop the cone down to near the floor level.
The flare of the cone prevents any more yarn from coming off than I deliberately pull off, and if I pull too much it's an easy matter to wrap a few coils around the butt, shortening the length.
When the original end is long enough, I then tie that onto the repair end and pull the knotted end through to the front.
When I'm doing short lengths like here for towels, I just wait until the original end is long enough that I can pull the knot through at a cutting line and I don't even have to needle weave the end into the cloth, just pin it into the already woven towel so that the join happens at the cutting line. :D
What can I say? I'm lazy!