Unfortunately, all employees are default at-will employees, meaning that they can be terminated at any time for any reason with or without any prior notice.
This stems from the employment at-will doctrine, which is codified in California Labor Code Section 2922, and states:
"An employment, having no specified term, may be terminated at
the will of either party on notice to the other. Employment for a
specified term means an employment for a period greater than one
Unfortunately, your employer is not under any obligation to inform you that you are an at-will employee and can terminate or suspend you at any time for any reason (including a bad or false one).
I also regret to inform you that you may not have the due process rights that full-time (tenured) teachers have under California law. This is because substitute teachers are considered 'temporary' employees and can be dismissed without due process of law under the following conditions set out in Education Code Section 44954, unless they work more than 75 percent of days in a given school year.
California Education Code Section 44954.
Governing boards of school districts may release temporary employees requiring certification qualifications under the following circumstances:
(a) At the pleasure of the board prior to serving during one school year at least 75 percent of the number of days the regular schools of the district are maintained.
(b) After serving during one school year the number of days set forth in subdivision (a), if the employee is notified before the end of the school year of the district's decision not to reelect the employee for the next succeeding year.
While permanent employees have due process rights and only may be dismissed for certain reasons, substitute teachers who work less than 75 percent of days in a year are at-will employees and can be dismissed with the discretion of the school board.
All that said, you still have a defamation cause of action against the girl's parents (although it would be very limited due to her parents' income). You also may have a cause of action against the investigator or school district if they spread false and damaging information about you.
If it's any conciliation at all, I strongly disagree with the state of the law and really wish I had better news to give you, but I hope you appreciate my honest and direct responses.
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Thanks and best of luck!