Switzerland is tiny- about the size of London. (circa 8 million)
Not quite sure what you mean re 'does that happen in Switzerland?'
But if you read my 'copy and paste' - if a significant group of citizens signs a petition re a new proposed Law or amendment to the Constitution- it doesn't have to be discussed in Parliament- it has to go to the popular vote. Be it on education, health insurance, new roads, the army, immigration, whatever...
In Februara 2014- a vote to limit immigration was very narrowly voted in- putting the Swiss Government in real difficulty, as it is in direct opposition to the bilateral treaties with Europe- threatening jobs, imports and exports, massive research projects, and so much more - and pointing to the difficulties of direct democracy. A more recent intitative to automatically deport any foreigner after 2 criminal offences, even minor- without any legal representation- was rejected!