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