It's worse than that. They often receive Bürgergeld, Wohngeld, etc. top-ups to their earned income, even if they work full-time, if they aren't married to wealthier Germans and they have low hourly wages.
So, taxpayers pay them to work, but they have full pension obligations.
A lot of work, that now needs to be done, is also a result of them being here. That's exacerbating the shortage in skilled labor.