How does being dependent on welfare impact the economy in a negative way?

The most substantial in my opinion is the GDP productivity lost by (persons with unemployment benefits), that otherwise would have been injected into the economy had this person been working. Places like Japan have very low unemployment rates because the law provides for very little unemployment compensation. Conversely, places like France have historically had more liberal benefits and have corollary higher unemployment rates.

In terms of living wage programs, they too may give the same disincentive to work, as there is some baseline of income that people can rely on from the Gov't. However empirically we have seen that WIC, Food stamps, Housing Allowances, act more as fiscal drains than they do against GDP. This becomes more of a budget impact than it is a decrease in the technology/productivity factor (a).

people depending on welfare = they are not working, or are not productive enough to receive living wage. It might be because people are lazy, or society does not provide enough eduction and training, or welfare is so high that it discourages work.

In either case, people on welfare produce less than financially independent ones, so GDP per person is lower than it could be.