POGS, in answer to your question, I can only answer for France. We were not obliged to register when we came here, but we did so at the local Mairie, who were well aware of our presence (but we live in a small community). We were obliged by law to register for tax purposes from the day we became permanent residents. We had to register for health cover and prove how we would pay for that. We have a health card which is checked and charged at all medical appointments. We are obliged to carry full ID (passport for us ID cards for the French) at all times and that is checked by the gendarmes from time to time in roadside vehicle checks. Any formal financial transaction requires ID and proof of residence such as an electricity bill. We have now got permanent residents cards and that involved a huge dossier proving health cover, residence, tax payments and sufficient resources (there are minimum levels) over a minimum of five years.
I think in a big city it might be possible to live under the radar for a while, but any involvement with authority would very quickly expose people who were not resident “in a regular fashion”. I don't know how many people get deported, but they would have no access to housing, schools, doctors or hospitals, which might amount to the same thing?