Similarly, I find the idea of the end of time to be weirdly unreal and impossible. It feels like time is not a thing that has a beginning or an end, and that it would just stretch and dissipate infinitely into the future.
You can still imagine that as an end, and define an end based on that infinite stretch. At some point, you can't tell the difference between before and after more stretching, and you'll never be able to stretch in a way that can be noticed.
There's no more events to happen, and more so, no ability for more events to happen.
Thats still likely an artifact of our models though, and that when you do to something like that, that new events start happening again
I'm not sure if Penrose suggests that time stops once there are only photons left. He says it is equivalent to the situation at the Big Bang and time certainly didn't stop there. In fact, in his conformal cyclical cosmology spacetime goes on indefinitely but just reboots regularily.