As for the covers in collector hands, I do not know a specific answer for Fairbanks, but it could be as simple as a secretary saving stamps for their own collection or for another collector. Also consider museums, archives, and historical societies in the past, as well as stamp & autograph collectors, sometimes separated covers from the letters and discarded/sold the envelopes as historically unimportant or to save file space. Do not be surprised to find the matching letters in an institutional collection.
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In terms of political power Fairbanks had significantly more during his one term as one of the two US Senators from Indiana (there are a total of 100 Senators - 2 from each state)
Minor corrections. Fairbanks served 8 years in the Senate consisting of a full term March 4, 1897-March 3, 1903, then the first two years of his second term, March 4, 1903- March 3, 1905, before resigning to become VP. Between the admission of Utah in 1896 and Oklahoma in 1907, there were 45 states. Thus throughout his Senate time, there were a maximum of 90 Senators, minus any vacancies.
Here is one of his preprinted Senate franks on a outbound cover:
