Dying from an infected tooth or a tooth infection is certainly possible if it gets severe enough but the good news is that dying from a tooth infection is rare.
Most tooth infection will usually go away on their own with home treatment such as using pain relievers, gargling with apple cider vinegar and gargling with mouth wash.
You can also use some tooth infection medicine on the infected tooth to help get rid of the tooth infection or gargle with some hydrogen peroxide which can kill the bacteria in your mouth causing the tooth infection.
If the tooth infection lasts longer than a week or two then you should see a dentist to be sure it's not a more severe infection.
Some tooth infections can cause heart problems so always get the tooth infection checked out either by a dentist or if it gets worse go to urgent care or the emergency room to have the tooth infection looked at and cared for.
Tooth infections can indeed become very serious if they're left untreated.