So it's probable that many Europeans could have encountered illegal immigrants without realising.
The common point is there a selection of low pay service jobs that attract illegal immigrants, who then become trapped. Some by debt and threats to family, and other more direct slavery. Anti-trafficking and similar groups have been warning of issues for years, and mostly ignored.
It remains a truth that the vast majority of immigration in Europe is legal, but there is a significant level of illegal migration. Thanks to the free movement of peoples within the EU, it is far harder to detect than before those border checks were pulled down.
Here is just one of a selection of pieces that have come up this week across all the press:
https://www.theguardian.com/law/2019/oct/25/trafficked-vietn...
Most of Europe is very different to the US in this regard. Without being legal/registered, you’ve no chance of getting the equivalent of an SSN, drivers license, opening a bank account, leasing an apartment or in some cases even buy a mobile phone. Consequently, the number of undocumented immigrants is minuscule.
I get the impression that in the US it mightn’t be unusual for the average citizen to encounter undocumented immigrant gardeners, nannies, etc. - this almost never happens in Europe.