How to change post status from frontend?

There isn’t much native functionality in WP to apply admin powers on front end. Front-end Editor plugin is usually great for such, but changing post status is one feature it seems to lack (maybe it’s worth suggesting to scribu).

So you are basically stuck with writing this from scratch – implementing JS on front end to make Ajax request and backend handler for it. Unless you need this functionality constantly and daily I would not bother with spending time on it.