I'm not asking this out of disbelief, but just out of genuine curiosity: What is the legal foundation that allows them to randomly search people who are simply going about their day? What happens whenever people say "no, you can't search my bag." ?
https://www.nyclu.org/en/cases/macwade-v-kelly-challenging-n...
> This case involves the NYPD's practice of stopping and searching subway goers without just cause. On July 21, 2005, the NYPD announced that it would begin a new program of searching the belongings of those seeking to enter the subway system. Since the program was implemented, the NYPD has searched tens of thousands of people without any suspicion of wrongdoing. On Aug. 4, 2005, the NYCLU filed a complaint in the District Court on behalf of five individuals. The complaint alleges that the NYPD program violates the Fourth and Fourteenth Amendments...
> On Dec. 7, 2005, the District Court ruled in favor of the defendants and refused the plaintiffs’ request for a permanent injunction. The decision stated that the random subway search program was not “impermissibly intrusive” and was constitutional. The NYCLU appealed to the United States Court of Appeals, Second Circuit. On Aug. 11, 2006, the Second Circuit upheld the District Court decision, stating that the program constitutes the “special need” exception to the Fourth Amendment.
From an NYT article about court decision in 2006, at https://www.nytimes.com/2006/08/12/nyregion/12search.html
> Passengers can refuse to open their bags and walk away, but they cannot go through the turnstile to the trains with bags they did not allow the police to search.
Fourth Amendment:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
What happens if you refuse a search is you leave the platform and get back onto the street where you're allowed to move about freely without being subject to search.