If I fractionally distillate A + B (miscible liquids); and if I obtain pure A in the distillate, does the distilling flask contain pure B or B + some A which manages to move backwards?

It really depends, if the liquids A and B have quite close boiling points, you will always have some which is left in the other.

For example, alcohol (b.p. 78 C) distilled with water (b.p. 100 C), you'll get the distillate as alcohol, but you will never get 100% pure alcohol.

Of course now something with boiling point 8 C mixed with water will most probably get the 'liquids' at 100% purity.

As you distill and collect the pure low-boiler A, the concentration of B in the distilling flask continuously rises. When compound B begins to distill there is essentially no A left in the flask. Still, you distlll compound B rather than just dump it out. There is always a little of each component in the liquids - theoreticaly. In practice very good separations are achieved with liquids of reasonably different boiling points.
Any component A still in the distillation pot did not "move backwards" however; it never left.

Ethanol and water form an azeotrope and the product, even following repeated redistillations will remanin 95% ethanol / 5% water. That's a different story from the problem under discussion.

Oh, my bad, I forgot about the hydrogen bondings binding the two >.<

It isn't just hydrogen bonding - alkanes and aromatics form azeotropes too.

With themselvs and with water as well.

Okay, that's new for me :o. Going to look more into it :)