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If I remember correctly, there should only be an APPLY ONLINE link, not an email address, unless the person posting the job added one in him/herself.
The idea that the person in the position currently is being fired is actually more common than you might think. Imagine how risky it might be if your job was to hire someone for a job that a person was going to be fired from; there are so many freaks out there, you have to be careful.
Either way, good luck, and just write a generic cover letter that highlights your skills and what you can bring any organization. The person who reveives the resumes know that without identifying themselves, the applicant may not be able to "show" them how he/she would fit into their particular organization.
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