The law meant that parahumans who had been convicted of enough prior crimes would be sentenced to the Baumann Parahuman Containment Center, rather than a regular jail from which they could easily escape. It normally protected parahumans who had no prior convictions from being sent there.
Parahumans who had committed particularly serious crimes (such as murder with intent) could be sentenced to the Birdcage outside the bounds of the TSPA, potentially even minors.
Gavel was sentenced to the Birdcage in the days before the three strike rule.
Marquis committed so many crimes that "the three strikes rule had been left well behind him" by the time he was captured.
Fleece was sentenced to the Birdcage based on the TSPA, while her partner Ramrod was sentenced to the Birdcage based on the magnitude of his crimes. However, they were broken out by Madcap before they could reach the Birdcage. This prompted Battery to gain her powers.
↑ 1.01.11.2"If the charges went through, she would face being charged as an adult. The three strikes protection act wouldn't mitigate things. I'd say the worst case scenario is execution, or indefinite detention in the Birdcage, but the best case scenario for her isn't much better." - Excerpt from Cell 22.3
↑ 2.02.12.22.32.4"Determining sentencing for this case is not easy. As your lawyer has no doubt made you aware, you do fall under the umbrella of the TSPA, or the three strikes act. At the age of twenty three, you have been convicted of no prior crimes. [...] I have decided that there is sufficient cause to sentence you outside the scope of the TSPA. Guilty on two counts, the defendant, Paige Mcabee, is sentenced to indefinite incarceration within the Baumann Parahuman Containment Center." - Excerpt from Interlude 6
↑ 3.03.13.2Marquis was next to arrive. His brown hair and beard were just now starting to get strands of gray in them, wrinkles at the corners of his eyes.
He'd been one of the scary bastards of Brockton Bay well before the Undersiders were even on the map. A guy who could go toe to toe with a full squad of Empire Eighty-Eight and walk away. He'd been successful enough to pay for hirelings and ruthless enough to execute them for failures. His path to the Birdcage had been very similar to the path that had almost taken me there; so many violations of the law that the three strikes rule had been left well behind him by the time the good guys finally won. - Excerpt from Extinction 27.3
↑ 4.04.1"No? Then why don't they send people like Über straight to the Birdcage after his trial, like they are with Lung? The amusing but relatively harmless villains get a regular jail cell, they inevitably break out before the trial concludes, and the cat and mouse game starts again. Sure, there's the three strike rule, and he'll get sent to the Birdcage eventually, but the people in charge have to maintain some plausible deniability." - Excerpt from Agitation 3.6
↑ 5.05.1The man with the beard was Gavel. Cell block leader. A vigilante who had gone after families, particularly spouses and children, all so he could break his enemies before his namesake weapon could. He'd been notorious in the days before the three strike rule or even the code. Even with that, people had lost patience with his ‘mission' when a villain had threatened to detonate a small bomb, and Gavel had called a bluff that wasn't a bluff. - Excerpt from Extinction 27.3
↑ 6.06.16.2"A year ago… well, it all started two years ago. There were two criminals called Ramrod and Fleece. The local heroes brought them into custody, partially because of my dad's work in tracking the pair down. Three strikes act applied to Fleece, and Ramrod was in for murder with intent.
"Finally, after about a year of court appearances and one minor appeal they managed to squeeze in there, it was decided. The pair was supposed to go to the Birdcage. Except someone broke them out." - Excerpt from Interlude 12½ (Donation Bonus)