Virus viability on fabrics
A VERY interesting question that I had to think a lot about, and frankly I couldn't come up with an answer.

Nevertheless, this article may have.

https://www.statnews.com/2020/03/19/coronavirus-survives-on-surfaces-how-to-protect-yourself/

"Viruses covered in “envelopes” have the most trouble surviving outside a living cell. On surfaces, the surrounding light, heat, and dryness break down the envelope, killing the virus. (Porous surfaces pull moisture away from viruses that land on them, accelerating the destruction of the envelope.) Most rhinoviruses have such envelopes; so do some influenza viruses. Norovirus doesn’t, enabling it to last longer in the environment."

Here are the author's relevant credentials.

Sharon Begley, senior science writer, covers genetics, cancer, neuroscience, and other fields of basic biomedical research. She was previously the senior health and science correspondent at Reuters, the science columnist at the Wall Street Journal, and the science editor at Newsweek. Among her favorite awards are an honorary doctorate from the University of North Carolina and the Public Understanding of Science Award from the Exploratorium in San Francisco.