The general consensus is that it depends on the size of the debt after the bank sells the property. If it is substantial enough to justify taking legal action in Ireland then they probably will, if not then they probably won't.
The latter scenario doesn't mean that the debt is not still owing, it is, but the bank may put it on the back burner.
However, as the EU is constantly in the process of harmonising cross-border taxation, debt recovery, etc. it is very likely that it may become a lot easier and cheaper to take action on retrieving this debt in the future.
If your friend takes this course of action tell her to be aware that the debt will never die, it will remain due. Like the Revenue, banks have very, very long memories and lots of patience when it comes to such issues.