Let’s say you’re some nomadic tribe 10,000 years ago and you get an abcessed tooth. What a happens to it without medical treatment? Do you die?
How about a peri-rectal abcess. Do you die?
Yep. Plenty of people still do die of abscesses. Some local treatments may have some positive effect, but if it’s too far gone you probably wouldn’t make it.
I recall from my introductory archaeology class that unhealed (i.e. fatal) dental abcesses aren’t uncommon in premodern skulls.
The modern day treatment for most abscesses is the same as it was 10,000 years ago: drain it.
Many abscesses drain spontaneously. Mother nature and all that. Tooth abscesses get big; the tooth falls out and the abscess drains. Many abscesses, including peri-rectal ones, will usually find their way to the surface and drain spontaneously, or with a bit of poking.
Deep abscesses (kidney; brain; lung etc) need modern therapy to do well for the most part.
Antibiotics are not all that helpful for ordinary abscesses, by the way. Incision and drainage is the key. Pus letting is a very satisfying procedure for patient and clinician both. But even incision isn’t necessarily needed if it finds its way to the skin and drains out on its own.