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Can an eldar player leave combat and embark in a wave serpent?

And can they use fire and fade to do this too?

Any unit* can embark after Falling Back.

In order to do this with Fire and Fade, the unit would need to be able to shoot in the shooting phase (i.e. have the FLY keyword or other ability to fire after falling back).

Eldar can use fire and fade to escape from CC, embark in a transport if they have pistols, and shoot them in the shooting phase.