Vinge's Marooned in Realtime comes to mind. The survivor's tech is close to what the singularity level was, but they "missed" the singularity and aren't improving their tech over the timescale of the story because of low population and other priorities.

"Missing" an intelligence explosion would be hard, if it drastically optimizes the solar system. In Vinge, this works because the exploding society simply disappears - implying that they're off in higher dimensions or femtotech or something. Other examples would be if the survivors are being simulated - there's a great story whose author I forget, about someone waking up after the singularity because he was an early brain scan and they just fixed him up now.