A citizen of the EU can get a registration certificate if (s)he [1]:
> is in paid employment
> is self-employed
> provides services in Denmark
> is a retired worker, retired self-employed person or retired service provider
> has been seconded
> is a student at an educational institution accredited or financed by public authorities, and s/he is able to support him/herself during the period of residence in Denmark or
> disposes of such sufficient income or means so that s/he is presumed not to become a burden on the public authorities
There is also a family reunification clause, which I've been told is very rarely granted. As for the registration certificate, it gives you a social security number, without which you are a non-person in Denmark.
In general, the previous Conservative, extreme right-wing supported government toughened the laws on immigration.
Ok Denmark, but overall the issue is valid. For example Finland has residency-based welfare aka no citizenship needed. Just read a headline last week claiming that Finland pays more welfare to Estonians than Estonia itself. Meaning Estonian citizens who live in Finland. Most came here to work but are now unemployed. You can't come here for welfare, but if you lose your livelihood soon after you are safe.