You have to break the sentence in to two:

1. Yellow fever has reappeared after nearly two decades -> is the main sentence
2. The disease that killed 4,000 Philadelphians in 1793 -> is a modifier that modifies the subject "Yellow Fever".
This modifier is roughly called noun + noun modifier. "The disease" modifies "Yellow Fever". Likewise, "that" also modifies the disease which is in turn the yellow fever.

The modifier "that" has two parts:
a. (that) killed 4,000 Philadelphians in 1793 and
b. (that) so ______ Memphis, Tennessee, that the city lost its charter

Both a and b are combined by "and" are trying to use "that" as the subject. Furthermore, these two - a and b - should be in parallel, which means they should represent the disease.

-> Through (a) we know that the disease killed 4000 in Philadelphia. Hence, b should resonate the same.
-> So... that... is an idiom which is used to express a particular purpose or consequence. Hence, "that" (the disease) so decimated (which means killed) Memphis that the city lost its charter. Terrorized and Corrupted do not resonate with "killed".

Great explanation

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