In just wondering thought. I would think surface life forms would be gone relatively fast (including us). Plant life would also perish due to absence sunlight and cold.
However, if looking at broad spectrum life forms. I would think simple life forms would be around for a long time, perhaps several millions of years.
Sub terrain life forms would still have geothermal heat. Also I don't think the oceans would freeze to the bottom for the same reason. There may be several kilometers of ice but still still liquid H2O under it.
As an example the life that exists around geothermal vent in the deep ocean is quite robust. to both temperature and pressure.
The same thing being with bacteria that exist withing the deeper earth.
I guess the planet would eventually wonder off in the direction of Proxima Centuria.
However, I don't think it would be a totally dead planet for quite a long time.
But, I am not going to worry about the Sun just shutting down on a moments notice.