What happens if a US Citizen Petitioning a Green Card for the mother gets Laid off from Work during the Application process?

You will need to update the I-864. Talk to an attorney, immigration is a complex process that involves much more than sending in forms. Many of us do consultations via Skype.

When the petitioner who filed the permanent resident application is out of work and no longer can fulfill the AOS requirements, he/she needs to update the already filed AOS and/or provide a co sponsor. It is better to consult an attorney to streamline the whole process

That means that the case may require a Co Sponsor potentially.

Contact a US immigration attorney about joint sponsor options.