Where does the remaining money of FP7 projects go? 'Framework programmes' (FPs) are main financial tools through which
  the European Union supports research and development activities
  covering almost all scientific disciplines.


I am a fellow of FP7 Marie Curie Initial Training Network (ITN) project. As a hosting institution, the faculty I work at got funding to support me and related research. Where does the non-spent founds after the project ends? Do they stay within the university or are they returned to the European Commission (EC)?
As usual, the answer is: it depends.

I have no experience with the Marie Curie programme, but for traditional FP7 research projects, the funding system worked as follows.

Your funding plan consisted basically of two large blocks: direct costs, and indirect costs. 

Direct costs included things like personnel (the largest part, usually), special equipment, or travel funds. For direct costs, the research institution needed to proof how they spent the money exactly. In case of underspending (for instance, if one planned for a postdoc but ended up hiring a PhD student), the left-over money has to be refunded to the agency (or, in some cases, can be transferred to another partner in the project). In case of overspending, the research institution has to cover the costs themselves.

Indirect costs, on the other hand, are a lump sum. They are calculated as a percentage of the planned direct costs (typically 25% for universities, iirc) and are meant to cover all the other costs of a project that are hard to account for exactly (things like the office space and heating for the people working in the project, etc.). These are paid out no matter what, and are not refunded. The research institution does not need to proof in any way that it actually spent all that money.

So to answer your concrete question: everything that is designated as direct costs in the ITN proposal and is not spent will go back to the EU. However, all the indirect costs associated with the ITN will stay with your host institution regardless of whether they spend the money or not.