This man was played by Stanley Kamel, who also played Mr. Monk's partner, Lieutenant Disher. The series finale was written with the knowledge that Kamel had tragically passed away, and it was a poignant way to honor his memory.
It's revealed that the man had been obsessed with Trudy and had been stalking her for a long time. He eventually snapped and murdered her, framing the crime to look like a random act of violence.