I didn't directly find a previous discussion about this, but currently the is_closed ufunc will always return False for LinearRings:

>>> ring = pygeos.linearrings(((0, 0), (0, 1), (1 ,1 ), (1, 0)))
>>> print(ring)
LINEARRING (0 0, 0 1, 1 1, 1 0, 0 0)
>>> pygeos.is_closed(ring)
False

This is following GEOS' behaviour where GEOSisClosed only works for LineStrings and not any other geometry (and thus also not LinearRings).

However, in Shapely, a LinearRing is also considered as "closed" (by simply hardcoded always True for a LinearRing):

>>> from shapely.geometry import LinearRing
>>> ring = LinearRing( ((0, 0), (0, 1), (1 ,1 ), (1, 0)))
>>> print(ring)
LINEARRING (0 0, 0 1, 1 1, 1 0, 0 0)
>>> ring.is_closed
True

PostGIS (https://postgis.net/docs/ST_IsClosed.html) seems to return True as well. It's not directly documented, but from a quick test (creating a polygon and extracting the exterior ring, as creating the LinearRing from WKT doesn't seem to be supported):

test_db=# SELECT ST_IsClosed(ST_ExteriorRing('POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))'::geometry));
 st_isclosed 
-------------
 t
(1 row)

Although PostGIS also returns True for Polygon