A common artifact searched for in looking for ETI is Dyson spheres, or some other megastructure whose purpose is to collect energy from the star. This structure was first suggested by Dyson 1961, but later expanded on by Kardashev 1964. Kardashev suggested that civilizations could be categorized into three different types, depending on the quantity of resources collected: a type I civilization would gather resources from their planet, type II from their star, and type III from their galaxy. Kardashev 1964, and later Annis 1999, and even later (sort of) Villaroel et al. 2016 argued that these different stages of civilizations could potentially be discovered! If a civilization were to harvest all of the energy from their star, then we would no longer see them (in the visible; the heat would dissipate as IR, leading to searches for this waste heat).
Villaroel et al. looked for disappearing stars. They compared data from Sloan and from archived data, looking for sources that were present in the latter but no longer there for the former. In essence, looking for disappearing stars. In the end, they found one potential candidate.
I said earlier that they sort of argued that this was a method for detecting other civilizations. I say “sort of” because they didn’t directly mention it. The thought is there, that this is a way to look for ETI, but the reasoning behind why ETI would cause a star to disappear is not mentioned. I’m sure there are a number of explanations that sci-fi fanatics could list, and maybe the authors did not want to potentially embarrass themselves by playing sci-fi author? Nonetheless, I’m not really sure, short of a Dyson swarm, what would cause a star to vanish. Feeding it to a BH?
That being said, I am becoming a fan of “parasitic” SETI searches. There is something about only needing to pay for time (not receivers or data) that really seems great to me! The data are already there, so why not go for it?