Certified GKH Gardening Expert
It sounds like you are going to have to remove the soil from the area, or container, if possible, and treat for a fungal infection.
During wet seasons, or if overwatered just a little too much, these plants can suffer infections quite easily. Make sure the soil is almost completely dry between watering, as these are quite drought hardy.
I would recommend treating the area, or fresh soil with dolomitic lime and wettable sulfur to help with spot treatment, and prevention for future infection. I give all of my plants these at least once per year for the same reason.
This collection of articles will help: https://www.gardeningknowhow.com/edible/herbs/basil