Not sure about Europe, but here in the US you can use the magstripe if your chip is broken. After three failed scans with the chip it lets you use the magstripe. I've always felt like it defeats the purpose - if the idea is that the chip is harder to clone, couldn't scammers just make fake cards with phony chips, and do that when they use it?

I'd say maybe it raises fraud alerts faster, but I had a friend who did this for every credit payment for like two months before she finally had them replace her broken card. (No idea why, since it was free.)