It's Summer Year 2, I've completed the season 1 storyline, and my character is married to Ken. I've started to notice that Friday nights he will go and stand in the doorway to the sheriff's office. He can still be walked through to enter the office and talked to. After some time has passed, he'll continue his schedule as normal.

I've only recently started playing again after picking up the season 2 dlc, so I'm unsure if that's the cause or if it had been happening for a while before that.