Boonkwan and Steedman (2011) train a parser that uses a semi-automatically constructed Combinatory Categorial Grammar (CCG, Steedman (2000)) lexicon for POS tags, while Bisk and Hockenmaier (2012;2013) show that CCG lexicons can be induced automatically if POS tags are used to identify nouns and verbs.
assuming clean POS tags is highly unrealistic for most scenarios in which one would wish to use an otherwise unsupervised parser.