In current Shapely, the base class BasecGeometry constructor can be called, creating an empty GeometryCollection:

>>> from shapely.geometry.base import BaseGeometry
>>> geom = BaseGeometry()
>>> print(geom)
GEOMETRYCOLLECTION EMPTY

However, if you want an empty geometry collection, you can also explicitly create one with eg GeometryCollection(). So I think it is not needed to have a working constructor for the BaseGeometry.

I know that at some point in geopandas we did use this to create an empty geometry, so it might be worth actually deprecating this in Shapely 1.8.

In addition, a more explicit EmptyGeometry was added (actually to address the issue that geopandas was using BaseGeometry() to get an empty geometry -> #514).
But since there is no "generic" empty type in GEOS, but only empty geometries of one of the specific geometry types (EmptyGeometry() also creates an empty GeometryCollection), in hindsight, this EmptyGeometry class doesn't seem that useful, and even somewhat misleading.

So I would propose to also deprecate this class (in favor of using the explicit constructors, like Point(), Polygon(), GeometryCollection(), ...)