The HUSH complex recognizes and silences foreign DNA such as viruses, transposons, and transgenes without prior exposure to its targets. Here, we show that endogenous targets of the HUSH complex fall into two distinct classes based on the presence or absence of H3K9me3. These classes are further distinguished by their transposon content and differential response to the loss of HUSH. A de novo genomic rearrangement at the Sox2 locus induces a switch from H3K9me3-independent to H3K9me3-associated HUSH targeting, resulting in silencing. We further demonstrate that HUSH interacts with the termination factor WDR82 and-via its component MPP8-with nascent RNA. HUSH accumulates at sites of high RNAPII occupancy including long exons and transcription termination sites in a manner dependent on WDR82 and CPSF. Together, our results uncover the functional diversity of HUSH targets and show that this vertebrate-specific complex exploits evolutionarily ancient transcription termination machinery for co-transcriptional chromatin targeting and genome surveillance.