Histone Deacetylase Inhibition
Yes, Sodium phenylbutyrate can upregulate the transcription of silenced genes by inhibiting the activity of Histone deacetylases (HDACs).
Histone acetylation performed by Histone acetyltransferases (HATs) helps in activation of genes, while deacetylation performed by HDACs is responsible for gene silencing. This makes HDACs a potent drug target to treat malignancies. 

The inhibitors of HDAC regulate the chromatin structure which loosens the chromatin and hence effect the binding of transcription factors to DNA.  This binding modulates the expression of genes playing role in cell cycle and apoptosis, thus effecting cell growth and differentiation. (Reference)

But this is not similar to double negative. Double negative is term used in embryogenesis, where a particular repressor gene is activated in specific regulatory state. (Reference)