Yes, she can. Many family members inhale asbestos fibers through contact with persons who have worked with asbestos, such as this situation where the husband brought the asbestos fibers home.
In this case, the Mother is absolutely entitled to seek benefits and compensation. We would advise contacting an attorney as soon as possible.
If you reside in Louisiana and need assistance, call the Gertler Law Firm at (504) 581-6411 for a free consultation.