The semantic investigation of relative clauses with indefinite heads is comparatively scarce in the linguistic literature. This paper discusses the attachment of relative clauses to unspecific indefinites, focusing on appositive modification. We have arranged the paper in four sections: (i) we examine German and English relative clauses that appear in these surroundings, seizing Sells’ observation on the close connection between appositive relativization and the discourse phenomenon of quantificational subordination (Sells, 1985) and expanding this idea to modal subordination (Roberts, 1989); (ii) we discuss the consequences of such data on the classical dichotomy of appositive and restrictive relative clauses and update the common diagnostics used for the differentiation of the two types of relative clauses; (iii) we will provide new and controversial data in German that gives rise to a reading we classify as “hybrid”, since it satisfies diagnostics of both restrictive and appositive relative clauses; (iv) finally, we will complete the picture by the discussion of an additional type of generic appositives which also attaches to unspecific antecedents.