These splitter work in the domain of light-pulses transmitted over a fiber. So you get 100% of the messages, but the flashes of light representing the bits will be much weaker. Probably this will mean that you have to put in much more effort to decode the signal than a usual network-device will need, and also probably means that you will have a higher number of errors in your data.
On the other hand, if you'd tap only a short distance downstream of the transmitter (or an inline amplifier), that 1% might be plenty, undisturbed by the distortions introduced further on the line, so probably that's the preferable tapping location anyway.
[I know that I'm oversimplifying a lot here and modern optical communication systems work much different.]
It depends on the power budget of the fiber link. A 3db splitter would tap 50% of the power, but if this was planned for in advance it would be easily integrated in the long haul network.
On the other hand, if you'd tap only a short distance downstream of the transmitter (or an inline amplifier), that 1% might be plenty, undisturbed by the distortions introduced further on the line, so probably that's the preferable tapping location anyway.
[I know that I'm oversimplifying a lot here and modern optical communication systems work much different.]