I played poker with friends last weekend, and at a late hour our chips in the poker case ran out. Than we bought chips from the chip leader. We gave him 10 euros and we got the equivalent in chips from him. That works right? Is it allowed to act like this?
As I pretty much always say in questions around a home game, yes go ahead, as long as something is agreed by everyone it's fine. It's important everyone agrees and that it's above the table as a deal. As Jon said in his comment, as long as the chips and cash match at the end it's all good.
Likewise as you said too, there is nothing stopping you from using something as a representative of a larger value. In fact there is nothing even stopping you from just putting cash on the table, i.e. if you're out of chips, just let the money play. This is something you'll see in Vegas too, 100$ bills can be allowed play, cardroom dependent (they allowed it in the WSOP cash tables). I'd personally be fine with paying the 10€ for the chips as long as the chip leader agreed to keep the 10€ on the table and not remove it from play.
At the end of it, chips are just a representative of a value that is agree upon by the game as awhole. You could use anything from cash, bottle-caps to different coloured lego bricks if you wanted once everyone agrees that it's fine.
Alternatively, if this is becoming a reoccurring problem, maybe buy another chip set would be a good investment :D