1. The DNA is sequenced. 2. Sequence data are compressed with a version of fqzcomp which has been modified to use/overflow a static buffer. 3. Something about this particular DNA sequence overflows a buffer in fqzcomp 4. The overflow contains some kind of exploit.

The paper is a little vague about where they inserted the exploit into fzcomp(https://fqzcomp.sourceforge.io/), but it does process the DNA sequence a block at a time. It tracks the frequency distribution of nucleotides so it can model them for compression. I hope the exploit was something really clever, like finding a DNA sequence that puts the encoder in a weird state, but it's also possible they just set BLK_SIZE to 1 or something like that.