Let \(G/H\) be a homogeneous space of reductive type with noncompact H. The study of deformations of discontinuous groups for \(G/H\) was initiated by T. Kobayashi. In this paper, we show that a standard discontinuous group \(\Gamma \) admits a nonstandard small deformation as a discontinuous group for \(G/H\) if \(\Gamma \) is isomorphic to a surface group of high genus and its Zariski closure is locally isomorphic to \(SL(2,\mathbb {R})\) . Furthermore, we also prove that if \(G/H\) is a symmetric space and admits some nonvirtually abelian discontinuous groups, then G contains a Zariski-dense discrete surface subgroup of high genus acting properly discontinuously on \(G/H\) . As a key part of our proofs, we show that for a discrete surface subgroup \(\Gamma \) of high genus contained in a reductive group G, if the Zariski closure of \(\Gamma \) is locally isomorphic to \(SL(2,\mathbb {R})\) , then \(\Gamma \) admits a small deformation in G whose Zariski closure is a reductive subgroup of the same real rank as G.