I have a similar issue: A GFCI outlet in the apartment we rent was pouring smoke, white smoke that smelled like ozone. The wall behind the outlet was hot to the touch.
My GF only found out about it when stopping by the apartment during a break from work. Luckily she works in a building just next door to our apartment building. She smelled a strange smell, the lights were off, and there was white smoke pouring out of the GFCI outlet in the kitchen.
She called the fire department, who checked the wall, and also felt the wall panel was still warm to the touch.
The lights were off in the apartment at the time. (we usually turn them off) and there has been NOTHING plugged into the GFCI plug for months.
So ,yeah, we are not staying there any more.

Any ideas on how something like this starts?

Some background: It's a 139 year old historic building that last had a interior structural rehab in the 1980s. Mixed retail and living units across three floors and a basement.

Ideas?