What is the risk of ignoring basal cell skin cancer and leaving it untreated?

Locally bad: Basal cell will get bigger. Get this taken care of now.

Basal cell cancer: Untreated, this cancer will slowly destroy the tissue around & under it. People sometimes lose an ear or a nose. Death is rare, but ulcers will slowly spread. Early treatment is curative and usually easy. Unless you plan to die of something else in the near future you will clearly benefit from treatment now.

Don't ingnore it!: Although basal cell cancers don't usually spread distantly they will cause extensive damage and continue to grow. They can spread along nerves and lymph glands. The larger they become the more difficult they are to remove and reconstructive surgery becomes far more involved. Do not ignore a biopsy-proven basal cell cancer and see a dermatologist for treatment advice.

It won't go away: These types of cancers don't go away on their own. When they are small, they are easily removed surgically, or sometimes even with a scraping and burning procedure called ed&c, or sometimes even with a topical medicine. With time, it will just get bigger and the non-surgical options start to disappear. The surgery required will become more extensive as the tumor enlarges. Get it while it is small.

Progression: It will continue to grow and will require a larger area to be removed when you do finally treat it. In addition it does have the possibility to metastasize.