What happened to all Mistborn during/after the fall of the Final Empire?

Question

During The Final Empire the Mistborn were described as rare, but not THAT rare. Each great house was supposed to have some. Elariel sent two just to kill Elend. The guard were "used to" seeing Mistborn in the night, so they were obviously not a very rare occurrence.

So what happened to them? In The Well of Ascension there seemed to be none except for Zane and Vin. After Zane's death Vin was considered virtually unstoppable. Were there any Mistborn with a hidden atium stash, they would have obviously tried their luck.

Did all other Mistborn die in the house war? Were there just 3 other Mistborn besides Vin and Kelsier during the Final Empire? Did all of them die because of a contaminated metal batch?

EDIT: Vin killed another one in the beginning of TWoA. Which actually makes Mistborn seem rather even less rare.

Answer 1

Besides the House War possibly dwindling their numbers, Mistborn were incredibly rare

While we don't know the exact number of Mistborn since the information about who is a Mistborn is a family secret (and a point of focus of Luthathel politics), we know Mistborn are incredibly rare.

They were so rare than even Major Houses didn't see arming their soldiers with metal as impractical. See Kelsier's thoughts when attacking Venture Mansion:

Despite Allomantic considerations, most noblemen still armed their soldiers with metal. Mistings who could Push or Pull metals were uncommon, and full Mistborn were even more so. Many lords thought it impractical to leave one’s soldiers and guards relatively defenseless in order to counter such a small segment of the population.No, most high noblemen relied on other means to deal with Allomancers. Kelsier smiled.

The Final Empire

As another point, Kelsier's effectiveness in provoking the nobles to war with his attacks rested in them assuming other Great Houses were attacking. Mistborn are so rare that an attack by one almost directly links to a great house:

“Venture isn’t sure who to blame,” Breeze said. “But because Mistborn were involved, everyone assumes that it was one of the Great Houses.”

“That was the idea,” Kelsier said happily. “The high nobility take Mistborn attacks very seriously—they have an unspoken agreement that they won’t use Mistborn to assassinate each other. A few more strikes like this, and I’ll have them snapping at each other like frightened animals.”

The Final Empire