Dear yumagreek,
The answer to your question is: not directly. Arizona is a community property state which means that inside of your marriage there exists a "community property estate" into which post marrital assets enter and are used to support the couple's lifestyle.
While the husband cannot be named on the litigation for the medical bills, his wages can be garnished post judgment with a supporting spousal declaration stating that his wages make up part of the community property estate and benefit his wife. Again, they may only do this after they have sued and OBTAINED JUDGMENT against his wife.
A bankruptcy may be in order for the wife. It is not necessary for him to file bankrupcty in regard to these bills, they are not joint debts - the hospital cannot pursue him alone after the bankrupcty has been discharged.
I hope this helps and I am sure everyone's thoughts in this forum will be toward your sister-in-laws complete remission. I am sure things haven't been easy for your brother either. Best wishes for the new year.
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