I didn't find much in my end-of-day search but the links below are a start on strikes and binding arbitration as a permissible alternative in Illinois:
How to Go on Strike
How to End a Strike
Several colleagues have mentioned binding arbitration as a desirable end. The Illinois Association of School Boards (IASB) has supported binding arbitration as an alternative to strikes while backing a law that would prohibit strikes by public employees.
Illinois Education Association has a FAQ on rights that mentions binding arbitration although the context is not clear: "All collective bargaining agreements are required to include a grievance procedure ending in binding arbitration and provision prohibiting strikes during the duration of the agreement."
Another source states that binding arbitration is "permitted" in Illinois:
ILLINOIS: Educational employees at all levels permitted to bargain under the Illinois Educational Labor Relations Act. However, several types of employees, including supervisors, managers, confidential employees, short-term employees, and students, are excluded from bargaining by statute. Impasse procedures include mediation and fact-finding. Arbitration is permitted. Strikes are permitted after several conditions set forth in the statute are met.Read the Illinois law here and here. Michigan's law seems much stronger and mandatory, according to this source. See also this link.
No talk of strike funds (probably none) or the option of binding arbitration. This happened when faculty struck at Central Michigan University. A judge ordered the instructors back to work but also imposed binding arbitration.
If there is any one out there who knows more about these issues, feel free to comment or, better yet, post a blog (with your name or pseudonym if you prefer!). I'm sure inquiring minds on campus would love to know more about the ins and outs of strikes, the alternatives, possible outcomes, etc.
I'd sure love to know more. Perhaps someone at the National Labor College knows? I'll try to contact them later.