So you're saying that an investigator looking for a specific type of evidence cannot find other evidence of the same crime? Are they then supposed to go back to a judge to say now we need to modify the warrant or get a new warrant? Do they leave people around so the new evidence isn't removed while the new/updated warrant is obtained? Are their time limits on the execution of a warrant?
“Fruit of the poisonous tree” is a legal metaphor used to describe evidence that is obtained illegally. The logic of the terminology is that if the source (the "tree") of the evidence or evidence itself is tainted, then anything gained (the "fruit") from it is tainted as well.
The doctrine underlying the name was first described in Silverthorne Lumber Co. v. United States, 251 U.S. 385 (1920). The term's first use was by Justice Felix Frankfurter in Nardone v. United States (1939).
Such evidence is not generally admissible in court. For example, if a police officer conducted an unconstitutional (Fourth Amendment) search of a home and obtained a key to a train station locker, and evidence of a crime came from the locker, that evidence would most likely be excluded under the fruit of the poisonous tree legal doctrine.
The fruit of the poisonous tree doctrine is intended to deter police from using illegal means to obtain evidence.
https://en.wikipedia.org/wiki/Fruit_of_the_poisonous_tree
See also “exclusionary rule”: