Humans have a strong will to survive, they wil always resort to whatever means necessary to keep alive.
When people lost their jobs and don't have any money they don't say "Well, I simply stave to death then".
What they wil do is resort to crime, and this costs more (in damages and law enforcements) than welfare does.
So from a pure financiel p.o.v. welfare is the best (cheapest) option, apart from gassing all the jobless.
And from a social p.o.v. it's the best solution too, but I know you care little about those arguments.