Perhaps they forgot to say that she stole two rolls of toilet paper from their restrooms last time she visited their offices, and also took the chance to write the f-word with lipstick on the mirror there. A hired expert confirmed it was in her handwriting.
I could go nitpicking on their message, however IMHO what they SHOULD write is:
1. Please be notified that Ms. X is no longer employed by us, and has no other business relationship with us, therefore since (date) she is no longer authorized to do anything at all on our behalf.
2. FYI she was discharged for having deliberately infringed our internal policies and regulations on different occasions. If you have any unfinished business with her, kindly let us know the details, so we can follow through.
3. Since she has your contact information, it is possible that she will attempt to hire you for additional work. Please be aware that she will not be doing so on our behalf, but on her own, so we will not be liable in any way for anything going wrong there. In short: from now on, if you take any assignment from her, it will be your own decision, at your own risk.
Since we value your cooperation, we thought it would be fair to let you know.