H4 EAD Is still under processing - Can I work Pending?

My wife’s current H4 EAD is valid until September 30th, and new application is filed on May30th, waiting for approval.
Every one is saying that she is not supposed to work after 09/30. Does it mean should she resign from company or can she take vacation (paid leave or unpaid leave)?
If she is OK to take vacation, she still be getting paychecks from her employer, is that Ok?

Please advice and any help is highly appreciated.

Yes, she should technically resign from the job. There is no automatic 180 days extension for H4 EAD holders. There are some companies that do something like unpaid leave, but the employer has to maintain I-9 compliance and it is slightly grey area. You need to discuss with your HR and legal and take necessary action.