The effects of extracting a single tooth on the face and soft tissues (the overlying muscle, fat pads and skin) are often overestimated. In a young person, the scaffolding of the face is still able to support itself and it is extremely unlikely that anyone would be able to notice a difference in the face after the immediate post-extraction swelling has gone away.
With age, there are changes to the structures that make up our facial features as well as structural changes in the skin. This tends to be the cause of sagging, drooping, more pronounced nasolabial folds (marionette lines) that are often unfairly blamed on recent or past extractions.
To be sure, having a large number of teeth extracted, especially at the front of the mouth will cause bony changes to the jawbones that will affect lip support and lip position, Replacing the missing teeth and supporting tissues with an appropriate prosthesis is a quick way to restore peri-oral volume.
If you are fit and healthy with no underlying medical conditions such as diabetes, if you are not taking any immunosuppressive medications or undergoing cancer treatment, then it is extremely unlikely that a dental extraction will cause any serious health problems. Post-operative complications aside, most patients have an uneventful healing period and return to normal within a few days.
