Yes, asbestos can be washed out of clothing - but it's only safe to do so in a very specific way:
Asbestos is a natural occurring mineral that occurs in nature and was used in building material because it has a property that slows down the spread of fire.
But then people learned it caused cancer!
When washing clothes that have come in contact with asbestos, ALWAYS rinse them out thoroughly outdoors - for example, in the garden with a garden house.
Otherwise, you could risk contaminating your house and washing machine.
There have been cases of people catching cancer from washing asbestos infected clothing on a regular basis, so please be careful!