Well. I don't like to assist cheaters,
but perhaps my answer can make some to NOT cheat
because of the risks because of in the Philippines it can be a serious crime, I believe even can get prison...
"My question is, will the wife or anyone can file any case to my friend as the former mistress of her husband?"
Yes.
But it would be against BOTH your friend and the husband.
" Or will it there be administrative offense to file for her now that she would like to work to the government agency again?"
Concerning RULES it depend of what policy each organisation have. Some don't even allow relations between two UNmarried, because of the frictions such can make in a working place.
Concerning carriere chance/damages it depend of who decide who to employ,
what influence the cheating husband/his wife have at the decider and how scared (or wife angry) they are.