there are two effects, the lean and the trail. A front-steering bike with trail is self-correcting through both effects. A rear-steering bike with trail will correct itself to a straight line as long is it is perfectly vertical, but will be unstable as soon as it leans. When it leans, it will go into a hard turn and collapse.
There are front-drive recumbents, but there are no rear-steering two-wheeled recumbents (it is possible to address the lack of lean stability on a tricycle configuration).