Nicotine is addictive. Smokers who stop will either need to find another source of nicotine or go through withdrawal. Some symptoms of nicotine withdrawal:
- Constipation or diarrhea.
- Fatigue, drowsiness, and insomnia.
- Difficulty concentrating.
- Depressed mood.
- Increased hunger and caloric intake
- Increased desire for the taste of sweets
- Tobacco cravings
So you should expect the results to be increases in sales of pharmaceuticals to address the symptoms. There would also be an increase in grocery and sweets sales, which would in turn cause weight gain and the associated health problems. I also wouldn't be surprised by an uptick in marijuana sales.
Tax revenues would fall. This would be especially bad at the state level. States often charge \$2-\$5 per pack. The sudden loss of this revenue would cause them to scramble for replacements.
In the long term, health care costs would drop but retirement costs (e.g. Social Security) would increase, as people would live longer. But in the short term, health care costs would stay the same. While quitting will always improve future health, most of the damage has already been done. People have to survive their current cancer before having a chance to avoid future illness.
Stopping cold turkey is hard. It's quite possible that a significant number of people will have just one more cigarette...ten times. That's a one in a thousand chance of survival. Expect tens of millions of deaths just in the USA. These deaths will reduce current tax revenues. There will also be drops in the costs of some services, but other services won't drop as much for years. Most people who smoke start when they are young, teens or early twenties. Smokers quit or die younger than others. So there is a distinct bias towards taxpayers among smokers. Social Security will be hard hit, as revenues will fall immediately while savings may not be realized for decades.
On the bright side, many more people will try the patch or nicotine gum. In each individual case, these are more expensive than cigarettes, but not everyone will use them. They may be cheaper overall.
If scientists have to figure out what is happening, it seems likely that nearly every smoker will die before scientists can figure things out. There are twenty cigarettes in a pack. That's a one in a million chance of survival. A typical smoker will smoke about a pack per day. If there are forty million smokers in the USA, figure on forty thousand surviving to learn what's happening.
If a warning is sent out as soon as it starts, more people will survive. But the truth is that almost all smokers know that smoking will be fatal but smoke anyway. It's unlikely that even an advance warning will prevent tens of millions of deaths. If everyone has just one more cigarette, twenty million will die. I think that this is optimistic. Four million survivors seems more feasible with advance notice.
Mortuary services will receive heavy use. Murders may increase--just plant a half-smoked cigarette on someone and there probably won't be an autopsy due to limited resources. There might be noticeable pollution from cremation. Graveyards will be full. Estate taxes will jump. People will have sudden windfalls. House prices will fall, as houses will suddenly become empty. Housing construction will fall due to the housing glut. There will be a recession as people adjust.
Some families will be harder hit than others. I can only think of one current smoker in my family, but I've known other families where all the adults smoked. Finding relatives to take the children might be difficult in those cases. Foster services would be overloaded.
Note that if this happened four years ago, Obama smoked. We might have had a President Biden. Biden might not have won in 2012 in the face of the resulting recession. Boehner smokes. Someone else might have been Speaker. I'm not going through the rest of the elected officials, but you may want to consider figuring it out for the setting of your story. That would be a reasonable follow up question: What legislative effects would there be on Cleveland, Ohio if 99% of all smokers suddenly died? Replace Cleveland, Ohio as appropriate. Consider giving an actual street address in the body of the question so as to allow people to work down all the way.
Note that my answer is somewhat USA-centric. I think that the same issues would apply elsewhere but of course the USA is what I know.