It depends, of course, on the country in question, since the consequences will be specified by that country's laws. In this case, my suspicion is that it doesn't matter unless and until your daughter wants to do something in Germany that a German citizen can do but an Irish citizen cannot. Even then, any other proof of German nationality would normally be sufficient, including a German national ID card.
Under the European Union's free movement regime, an Irish citizen can only be excluded from German territory for a very limited number of very serious reasons, so it is very unlikely that your daughter would ever find herself in a position where she needed to prove her German nationality to avoid removal to Ireland. If she did, however, she would again need some proof of German nationality, though it would not need to be a passport.
Certain government employment may be limited to German citizens, as may be certain political offices.
A quick reading of the Personalausweisgesetz suggests that Germans who reside abroad are exempt from its requirements. If that is correct, then there would be no consequences for failing to have a German identification document, unless even a short visit is considered a period of residence for the purpose of the law. If your daughter is over 16 then you may want to look into that further.
