Your experience is one I had suspected might happen, especially since many of the Turkmen lived in areas where water was a valuable commodity. And you did not even need to sacrifice a valuable antique weaving!
Some dyers may not have rinsed the newly dyed wool thouroughly enough to prevent eventual runs.
I think the common perception of nomads wandering the parched wasteland is a bit far fetched, since they occupied and defended the most temperate areas they could. They did not live in a tropical paradise, though, and it is quite likely that there may not have been enough water to properly rinse all of the wool all of the time.

Patrick Weiler

This seems like a good time to update the interim summary I posted a few days ago, in which I listed the explanations for stray reds that had come up in our discussions. The first five are a repeat, reproduced here for your convenience:
1. The one everybody knew about before we started, color runs from using a synthetic red dye in the piece, common in 20th century production.
2. Natural variation in the color of nominally ivory or white wool, exemplified in Amos Bateman Thacher's Yomud.
3. Red wefts peeking through white or ivory pile, as in my torba (trapping?) and, perhaps in the Tekke germetch in The Rickmers Collection.
4. Staining from dyes originally on young rugs that, one way or another, had colors that ran onto older ones, as exemplified by some of the rugs in the Dudin collection in St. Petersburg.
5. Photographic artifacts, which Wendel notes in a (non-Turkmen) bag in his collection and which occurs in at least one Salor bag from St.Petersburg's museum.
6. Runs from cochineal reds, which apparently happen now and then.
7. Runs from madder that was inadequately rinsed from the wool after dying.
8. Runs from washing old (natural dyed) rugs in boiling water.

Steve Price

You forgot: Grandchildren redesigning the rug.

I think it's useful to make a difference between badly executed and handled or rightly executed and handled.
At the and of this story, all "bloody" rugs are ok.

Well done natural dyes do not run.
Well done chemical dyes do not run.
They leave traces, marks, on the surrounding white wool after 100/150/200 years.
I would.

Best regards,
Vincent Keers