Keep in mind that small molecules tend to be more soluble in water than larger ones, so it's likely that those pieces of dye molecules will go into solution when the clothes are washed, but certainly not all of them.


To learn more about how cleaners actually work, spend a few evenings at the web site of the Soap and Detergent Manufacturer's Association website at:

[url=http://www.cleaninginstitute.org/]

PS:
Did you know that our word "soap" almost certainly comes from the name of Mount Sopa which lies not far from Rome?

During Roman times, Mount Sopa was the traditional place you went to ask a favour of the Gods and sacrifice a small animal to them in the hopes they would grant your request.

Roman women noticed that washing their clothes in the streams that ran off Mount Sopa after a rain would get those clothes cleaner than washing them anywhere else, or washing them at any other time.

It is now believed that the animal fat that dripped onto the sacrificial fires and combined with the ash of the burned wood formed a crude soap, which then dissolved in the rain water run-off to put some soap into the water the Roman women were using to wash their clothing. That's why the clothes were noticably cleaner.

It is also known that early Romans combined animal fats and lye to make a form of soap which they applied to their skin as an ointment, but there's no written record of them ever using that soap for cleaning purposes.