They collapse. One reason or another. The more interesting thing is how that shakes up the rest of the Americas. It's arguable that the Incas, the other premier power on the continents, could have taken over the Aztec Empire. Distance alone makes this problematic.
Eventually a successor Empire will probably take the place, just due to lack of comparable nations in the region to move in. What's more interesting is where refugees go. We have proof that the Aztecs did trade with the Incas and the relative stability of the Incas, will be appealing to the population. However another number will settle north along the coasts, away from Central America.
I'm not sure what sort of nations/tribes existed in the North or their level of development. It's a debated issue, even to today. What will happen regardless is greater integration between the Native American communities. More trade, more conflict, more advancement.