The town council of the village in the canton of Aargau said on Friday it would welcome a Christian family of five asylum seekers from Syria in January, reported Swiss media.
The council has asked the population of 2,200 residents to come forward if they have vacant accommodation to offer to the family, said news agencies, however as yet no one has done so.
Oberwil-Lieli, one of the richest places in Switzerland, hit the headlines in May this year when its residents voted in favour of paying 290,000 francs a year to the canton instead of agreeing to house their allocation of just ten asylum seekers.
The decision caused bitter divisions within the village but was supported by its mayor, Andreas Glarner, a Swiss People's Party (SVP) hardliner.
Glarner said at the time it was the “civil duty” of Swiss citizens to “resist” the Swiss government's policy on refugees, which stipulates that all cantons should house a share of the total number of asylum seekers accepted by Switzerland.
“Switzerland must close all of its green borders with barbed wire,” he said.
Despite this change of heart – which the council said residents did not object to – the village is still five people short of fulfilling its obligations.
The other five asylum seekers who should be housed in Oberwil-Lieli will instead be taken on by a nearby commune, said the council.
The village will also give a sum of 50,000 francs to a private organization helping refugees in Greece and Turkey, it added.
Last year the Swiss federal government said it would accept 3,000 refugees from Syria over a three-year period.
According to the latest figures from the Swiss Migration Office (SEM), the number of people requesting asylum in Switzerland is slowing.
In October 2,096 asylum applications were lodged, 4.1 percent fewer than in September and nearly 56 percent fewer than the same time last year.
The majority of asylum seekers in Switzerland are from Eritrea.