A dead tooth can sometimes smell but not all dead teeth will smell bad or smell at all depending on the infection.
Sometimes a tooth infection can spread too far before the tooth even smells which can cause other health issues.
If you have a dead tooth or tooth infection even if you have no smell to it you should see a dentist about it to make sure you don't have an infection that is spreading.
A dead tooth can also cause gum disease which can lead to bad breathe as well as a bad taste in your mouth.
If you do have a bad tooth that smells or a dead tooth that is smelling then you should have it checked out to make sure it's not an infection that can lead to other serious health issues such as heart disease, heart attack etc.
Tooth infections can become serious enough to cause heart issues so always get your teeth checked out when you have a tooth infection.
You can also gargle with apple cider vinegar to help kill bacteria but still get it checked out.