> What should one think about this?

It depends on how badly you want/need this particular job, how much you trust this employer and what are the norms in your locale and domain. Consider your alternatives before making this decision.

I can't imagine doing this in my part of the world and my domain (US, software). If someone wants to hire me, they would need to pay for *all* of my work.

But working a free month is not typical in my space, and I'm not desperate for a job. Your mileage may vary.