"a month in welfare"

Is this TANF? "Temporary" help.

"Will filing the tax return affect their welfare."

Everything you asked means you need to do the research. No one on the internet can answer such specific questions. They are your clients, and you know the details that matter.

You might start here:

https://www.usa.gov/welfare-benefits

I would point out that you file taxes for the taxpayer if there is a requirement for them to file, or when filing gives them some benefit such as refundable credits. You also file for the facts and circumstances, not out of consideration for what else might happen.