Good question. Depends on the empire and the qualifying relative (place of birth, right of residency, possibly even their ethnicity).

For example, when the Austro-Hungarian empire collapsed, those born in territory of modern day Hungary (when it was Austria-Hungary), received Hungarian citizenship, whereas those born in the new state of Czechoslovakia received Czechoslovak citizenship.

Those individuals are now potential qualifying ancestors for some of their descendants to apply for citizenship by descent in Hungary, Czechia, and Slovakia, respectively.