When a citizen does something "questionable" overseas....what is the Govt's responsibility to help?

Everyone is hailing the release of the prisoners from Iran, but it does raise an interesting question.

What is the Govt's responsibility to help if one of its citizens does something questionable overseas?  It extends past the hikers in the desert of Iraq that crossed over into Iran (how stupid do you have to be to think that's a good idea), or the aid worker in Syria that got captured, raped and then killed by ISIS.

This covers a whole slew of issues that the govt eventually has to deal with.  For example.  The aid worker.  Supposedly, the CentCom had laid on a rescue mission if they could pinpoint her location.  You can bet that someone would probably get hurt and maybe killed in the effort.  Is it fair to ask a Soldier, Sailor or Marine to risk his life to save someone that has lollipops in their eyes and wants to save the world no matter how dangerous it is?  Is it fair to the families of the service members that go into harm's way?  What about the prisoners in Iran?  Should we allow the fact that they have our citizens affect our diplomatic approach to them?

With more and more people having dual citizenships, believing that they're global citizens first and Americans second, it stands to reason that we're going to see an uptick in people doing stupid stuff for stupid reasons and then expecting the govt to pull their chestnuts out of the fire.

So where does personal responsibility end and govt assistance/requirement to help begin?