How borders are drawn and enforced has far-reaching consequences, whether we live on either side of them or halfway across the world.

On Sunday, Switzerland is voting on whether to cap the number of immigrants to just 0.2% of its total population of 8 million, which would restrict the number of people coming in to about 16,000 people a year. Whether it succeeds or fails, this latest plebiscite—named after the 40-year-old Ecopop movement that seeks to link protecting the environment with slowing population growth—is just latest Swiss effort to keep the outside world at bay.

In February, the far-right Swiss People’s Party mustered enough signatures to get a national referendum on introducing immigration quotas—and won by a slim margin, throwing relations with the European Union into flux. Switzerland, famously neutral, is not a member of the EU but has several agreements allowing citizens from the 28 EU nations to live and work in Switzerland and vice versa, as well as travel passport-free.

The referendum result violated those agreements, and the government has no idea what to do. The result of the February vote has yet to be implemented.

Switzerland is at the center of Europe geographically, and outside of it politically. But the worst attacks on the principle of free movement are coming from a country on the geographic edge and political heart of Europe. Earlier this week, British prime minister David Cameron announced plans to force migrants to wait four years to claim certain benefits. For this plan to work, the other EU leaders will have to agree with it—and this much-retweeted Czech reaction, harking back to WWII, shows it isn’t going to be easy:

Any changes to the basic right of free movement within the EU must be endorsed by the rest of its members. Cameron had floated plans for a Swiss-style migrant cap, but these were a non-starter, perhaps because of a German intervention. Now, with nothing more up his sleeve, Cameron said he would “rule nothing out” if the UK didn’t win backing for his new, more limited proposals—implying that he would campaign to leave the EU in a future referendum.

Why is Cameron risking the UK’s four-decade-long EU membership? The rise of the anti-immigration UK Independence Party (UKIP), which recently entered parliament. UKIP wants to leave the EU. Cameron is trying to find a way to stay in without losing an election.

And the UK’s shrinking mainstream parties aren’t the only ones in Europe facing threats from the left and right. In France, the Front National’s leader, Marine Le Pen, is being hailed by the Austrian and Dutch far-right as the future president of France at this weekend’s annual party conference. In Greece, already in parliament (paywall), to Brussels.

Almost 25 years after the European Union was first created and free movement was enshrined as a right of all its people, immigration is becoming the most important issue to voters across a region with high unemployment and a perpetually weak economy. But how much can they pull at the fabric of the EU before the whole thing falls apart?