A woven wrap is a long length of material with a loose weave, this enables the fabric to keep it's strength and shape while having a good amount of 'give' along the bias (diagonal). These qualities make the fabric ideal for carrying a baby, allowing mama and bubbah hours of comfortable walking/playing/shopping :-D
The downside of this loose weave is that individual threads can become snagged on clothing, car doors, velcro... and be pulled out of the weave, causing a nasty little loop to form on the surface of the fabric. In the most extreme incidences these threads can snap ad become broken, or can even form a hole :-( A broken thread is, unfortunately a hole waiting to happen. Once a hole forms in fabric it's much more liable to a tear... so for many people a broken thread is the death if a wrap... because they can't trust a 'hole waiting to happen' to carry their baby... fair enough! ... but they can be fixed :-) fixed broken threads are not always pretty, but they are safe if done correctly :-)
Identify both ends of the broken thread, in the left hand image you can see one tail of the broken thread, but the other end is still woven into the fabric, you need to use a needle or pin to unweave the other, hidden end of the broken thread so you've got both to work with.
Thread a needle with the longest loose thread and reweave it into the fabric. With some wraps this is easier than others. With the wrap on the right I was able to mimic the weave of the fabric more or less exactly, but with the more complicated patterned weave of the indio to the left I had to just do my best...
Rethread your needle with the 2 tails and push the loose tails into the weave, like you did before. This time you might need to use the blunt end of the needle since you're probably running out of 'tail' so be careful!
Trim and enjoy!
Once you've woven as much tail into the fabric as possible you can (CAREFULLY!) trim the raggedy end away! FIXED!! yeyeyyeeeyyy!!