Swedish to English Other Social Science, Sociology, Ethics, etc. Personal document

This phrase (which I suspect to be an abbreviation) occurs in a so-called "ämbetsbetyg" issued in Finland, in the context:

XXX, född (...), vigd med YYY, född (...) in ZZZ, leva härst.

Could it mean something like "living descendants"? The spouses had a girl, mentioned in the document.

Thank you.