score:4
I highly recommend not to overstay only to save a couple of euros.
If you save a huge amount of money (which I doubt) you can consider to do a city trip outside schengen area and so save those 3-4 days you need. However, this will be probably more money in total.
Edit: Relaxed is right, I somehow forgot this detail in the first part of my answer. Visa extension is only possible in the way o.m. described
Upvote:-1
As the other answers point out, your girlfriend's life will be much easier if she leaves the Schengen zone on time. Let me add that there is a cheap flight using Air Europa, Madrid to Lima, Peru (below $1000 US most days). If you first holiday in a place where you can connect to this flight airside in Madrid, she could stay longer; there is no visa needed for the airside connection. Example, Rabat or Tangiers, Morocco have such connections, and Morocco has visa-free entry for Peruvians. So to the European countries @phoog gave in his answer, minus UK/Ireland. I just couldn't find a cheap connection from the countries in his list that I tried.
Upvote:4
but the cheapest tickets are 1 or 2 days after the date she has to leave.
Then don't buy the cheapest tickets, buy the cheaper ones. Problems caused by overstaying your visa are far more costlier than the cost of paying some extra money for tickets.
Nobody is going to extend your visa just because you like to save some cash.
Upvote:4
There might be reasons to extend a visa, for humanitarian or medical reasons and the like, but just saving money is not among them.
But most likely user Hanky Panky is right -- just get out within the time limit.