So I've watched the original Mad Max trilogy with my girlfriend to prepare for the new one, and so we've watched the IMHO trainwreck that Beyond Thunderdome was.
I simply didn't understand the end. Max caused untold destruction in Bartertown, bit Auntie in the ass several times, earlier was sentenced to death, and yet, captured, at the very end, she just laughs, "We make a good team" (or something along those lines) and just let him stay there. To survive. Why? Did I miss something?
Aunty Entity has a great deal of respect for those who survive. She rules with an iron fist, but she always gives her victims a chance, a way to persevere. This philosophy is reflected in her initial discussion with Max:
AUNTY: Do you know who I was?
(Max nods in the negative)
AUNTY: Nobody. Except on the day after, I was still alive. And this nobody had a chance to be somebody.
AUNTY: So much for history. Anyway... water? Fruit?
AUNTY: Congratulations. You're the first to survive the audition.
Her philosophy is also reflected in many of the laws she created, such as the Thunderdome itself and the Wheel of Punishment - both of which allow for a way out.
So, despite the havoc that Max had caused her by the end, Aunty was forced to acknowledge his own resourcefulness. He had not only managed to survive the Gulag punishment, but returned to tear down Aunty's empire. This was a man worthy of her respect, and she acknowledged that by sparing his life.
Slight correction: she says "aint we a pair"
The leaving him alive unpunished is a sign of respect for his defiance and his bravery.
Though it could also be argued is leaving him alive an act of mercy? he wont be able to go back to barter town and the wasteland isn't the most friendliest of places. He in all likelyhood will suffer there far more than anything auntie could have done.
I suppose the main reason is George Miller didn't want his character dying in the end, so that was that, but if we can put that fact aside, I think Auntie Entity isn't a villain. She's an antagonist in this story, but she's not really a bad guy. Comparing her to Immortan Joe, for example, that guy is barbarian warlord. Any order and structure he brings to society is almost incidental to him having power. And you see that demonstrated, he's got a near-dead mass of common people begging for water, he leads a group of fanatical teens and men into battle, he's got a harem, he's not a responsible leader, just a warlord. Auntie is like the opposite of him, when she found power she built Bartertown. She made rules to help keep order and peace there. She lives in a large tower, not a mountain stronghold. So in the end it feels like it makes sense that she'd let this former policeman, defender of children and the weak, and generally good person live even when he's defied her. She's not really a destroyer or a killer, it's not what she prefers to do.
A hint is that Aunty is not a bad person and closer to Max than to the Toecutter or Humungus or Immortan Joe. She says she would do anything to protect civilisation and killing someone in cold blood would not be that. Barter Town was a flawed but genuine attempt to help people and a lot of it meant well. A lot different to Toecutter or Humungus. Immortan Joe is somewhere in between.
Anyone who threatened her position of authority there, had either left, been killed, or was no longer a threat to her. In a way Max helped her. All she wanted to do was remain in control. In the end that's how she remained. She had no reason to kill him. Also, as pointed out in another answer, she left him there in the wasteland, which really was no favor to him.
