Patch fiber is usually using Class 1 or Class 1M lasers which are entirely safe to look at. Also the light spreads out very rapidly at the end of an unterminated fiber because there's no lens to focus it. So don't hold it directly up against your eye but like a foot away is fine. The lasers are less focused (i.e. cheaper) and the multi-mode fiber is wide so it spreads out very quickly. You can't actually see the IR light, the red light you see is just sidebands of the signal.

Fiber used for long hauls is much more powerful but uses a wavelength that the human eye is very good at blocking (so your eye dissipates more of the energy but what does get through could damage your retina). There are systems that will decrease the power if the link is lost (cut or unplugged) to protect eyes. The light will still dissipate in free space (because there's no lens) so you should be safe from a distance. Single-mode fiber uses a more focused laser and more narrow fiber so it will spread less over a free space distance so don't get too close.

Always better to just use a light meter (or a phone camera) if you're unsure but also just holding the end of the fiber against some paper or your palm may reflect enough of the visible light to let you know the fiber is live.

Just in case, always use the same eye to look into these things.

"Do not look into laser with remaining eye"

As an intern moving data centers the old networking guy told me to look into them; I used my right eye and now my eye is 20/40 a decade later whereas my left eye is still 20/20. I did hold it up to my eye because it was hard to see..

Some scientists used to look at the beam emitter to adjust the aim of old particle accelerators. The story I heard was that some of them eventually developed cataracts as a result. Come to think of it, with today's medical technology that's a lot less awful than punching holes into your retina with a laser, but I think the result back then was eventually blindness.

I met a scientist who looked into a particle accelerator; it was intention, part of a self-experiment to establish whether high energy particles can cause scintillations in the eye. In his case he very carefully calculated how to get a safe dosage.

On the other hand there's https://en.wikipedia.org/wiki/Anatoli_Bugorski