A dermatologist determined that silicone is now leaking from my ruptured 40+-year-old implant through my skin. Is this likely?

A ruptured silicone implant, especially one that is so old, should be removed immediately. This is for your safety as it can cause serious complications to your health if it is left in.

Although this is not likely that the silicone is coming out of your skin unless there is a history of trauma it is possible, silicone may have also
leaked to your lymph nodes in this situation. Most silicone ruptures are
contained within the breast implant capsule. The treatment is implant removal
and capsulectomy typically with an implant exchange. The silicone implants
today are highly cohesive and tend not to leak as you described.

It is likely that leaking silicone is causing these changes in your skin.  You should have them removed immediately.  The longer you wait, the more chance the silicone will damage your skin.

Agreed. Your silicone implants are ruptured and need to be either removed and replaced or simply removed. Go see you board certified plastic surgeon. Depending on the manufacturer (and the longevity of the implants), there is likely some financial assistance to help you take care of this.

I would check with your provider but removal for medical reasons without replacement is not considered cosmetic. Dr Corbin

If what you say is true, then the skin will erode until the implant material becomes exposed. It may then get infected. You want to remove the implant in a controlled way or you may wind up in an emergency situation.  . Prevention is more important than money, in my opinion this is an emergency now and you should see someone about it soonest.  Medicare may cover the removal, but not replacement.