I don't trust a lot of things I used to believe just a few years ago.
No, I don't think anyone in the fed, state, and in many places, local much cares about vetting voters. The only thing that might doing anything could be whatever automated voter registration system they've got setup... if there even is anything that actually does it vs volunteers.
I don't know about the tax collection part. I think the IRS is too big and bureaucratic to care one way or another about getting extra taxes from someone using a duplicate SSN... Actually, the more I think about it, the more it seems like it they don't vet that very well either. Example: Alfredo A. is a valid US citizen, has a job, does his taxes, etc. Alfredo B. somehow gets A's SSN and uses it for his job. If Alfredo A. were to ever get audited, he'd get busted for not including what the IRS would see as a second W-2(in reality Alfredo B's job) on his taxes. There's a good chance B's extra income would bump A up into a higher tax bracket and he would owe more. If the IRS really cared, they'd be coming after A for that extra income that wasn't reported on his taxes.
What's more likely is that the IRS just doesn't care enough to pay attention to those things.