SPOILERS AHEAD YOU HAVE BEEN WARNED

As you find out after you finish the last chamber, you have two paths you can choose. You can either place a few portals and leave the facility, or you can go back into stasis. Below are my interpretations of what each ending means. Feel free to leave comments if you know more specifics than I do.

In this ending, you follow instructions and you go back into stasis, with the expectation that you will be woken up in time to prevent the fatal incident that will destroy the Aperture Science facility, which occurs between the present and future timelines. This incident could be one of several known events, such as Chell's destruction of GLaDOS in Portal, but if it is a known event, then the most likely option is when Wheatley takes over the facility in Portal 2 and almost destroys it, so you would be trying to stop Chell or Wheatley in that case. There is also a chance that the incident is not something previously covered in the lore.

The short, boring, and most likely explanation of what this ending implies is that you were woken up and did stop the threat, but it all happened off-screen without involvement from you, the player. This is strongly implied by the escape ending, since the future timeline is fine in every other part of the game except when you take the branching path and choose not to stop the looming threat.

Another possibility is to assume you did wake up, and you did try to stop the threat, but you were unsuccessful. Instead, you were able to somehow pave the way for Chell to save the day in one of the other Portal games, but to what extent would not be obvious, since the identity of the person leaving all the notes and drawings behind in Portal 1 is known to be Doug Rattman. This would help explain why subject 4509 is not directly seen in any other Portal games.

However, if we assume that the player character is actually never woken up in the stasis ending, there is more to think about.

It's fair to say subject 4509 was taken from the same vault that the robots manually open at the end of the Portal 2 coop, so if you were supposed to be woken up at any time after the automatic lock on the vault door stopped working and before the robots opened it, there would have been no way to retrieve you from the vault. This is the most logical explanation and fits the canon nicely.

Some other possible explanations for your slumber include a glitch or complete power loss in the AI responsible for waking you up, or that the AI woke up the wrong test subject (as there are thousands to keep track of). Your own death or a failure in the stasis chamber could not be the reason, since the regeneration system that canonically brought you back to life was working in the future timeline.

In conclusion: The fact you never see anything after you go into stasis makes it easier to fit the story of Portal: Reloaded into the existing lore, and I respect the developers for trying to make it feel canon.

In this ending, you divert the funnel, travel to the future, the AI in your head fails from lack of power, and you make it out of Aperture Science. The triple portal device stops working once you are out of the facility, and several standard zombies (humans taken over by standard headcrabs) are on their way to get you.

For those who don't know Half Life, Headcrabs are omnivorous, parasitic alien organisms that latch onto and control human hosts using their claws, mouth, and beak. While the human host can sometimes be saved if the headcrab is removed quickly enough, such a takeover usually results in death of consciousness. The resulting creature is hostile towards other humans.

Obviously, you never get to stop the incident as you were supposed to, but it doesn't really matter because we aren't sure it gets stopped in the stasis ending, either. Similar to the Half Life franchise, you have the potential to get away from the zombies or kill them, but since you find yourself in a forest setting with a defective portal device and likely no other weapon, I'm not sure how well you'll fare. Furthermore, based on Portal 2's ending, it is unlikely you can re-enter Aperture Science after getting outside. A full-blown headcrab zombie apocalypse is not likely what is implied; it's far more likely that this is an abandoned patch of civilization at least several miles from any humans that haven't been infected by headcrabs. While I would say the protagonist likely dies, it's anyone's guess; feel free to use your imagination.