As I understand it, because of the European Union’s rules about free movement of labor any EU citizen can work everywhere in the EU legally with very little pap

As I understand it, because of the European Union’s rules about free movement of labor any EU citizen can work everywhere in the EU legally with very little paperwork. Legal migrants are given full access to the welfare state from their first hour of work. Most migrant workers are therefore from Eastern Europe, and can work there legally. I don't know about Sweden, but here in Norway enforcement is pretty strict. Industries that the government considers especially prone to illegal activities, like construction, are inspected regularly. There is also a system of forced tariff (minimum pay, requirement to pay extra for overtime, and other standards), and companies can be hold collective responsible for what their subcontractors does. Employers that don't follow the rules face large fines, confiscations and prison. Every worker has the right to collective bargaining. Illegal immigrants can of course be deported, but because there is no place to incarcerate them until they can be sent home, the government mainly focus on deporting criminals and thus with a known home address, not scooping up illegals where their may work. However we have a new government that may make changes to this now.