I know what happens to fabric, but don't know how to work the computer very well!! LOL I had it written to post, then lost the answer!. Well, here we go again.
The heavy scent of cedar is thought to mask the scent of wool, which is the target for egg-laying moths, effectively preventing her from laying her eggs. It doesn't repel them so much as it confuses the scent, in which case lavender, tansy, or rosemary will work as well. There is very little evidence that cedar actually works. The damage to wool is caused by the moth larvae, not the moth itself. The Eastern Red Cedar will kill small larvae over time in an airtight cabinet.
The real problem with storing fabric directly on the wood in a cedar chest, is that the lignon in the wood is an acid and will weaken the fabric over time and turn it yellow. So it's a very good idea to wrap those precious quilts and blocks in acid-free paper and store them in a plastic box. I'll have to research the effects of the cedar scent on fabric, because I don't know if there is any effect at all.