H4 can stay upto 240 days after i94 expiry - legally
USCIS says that a person is considered OUT-OF-STATUS after 240 days of i-94 expiry.
This too, when you have filed the extension application before your i94 expiry and have not received any final result.
USCIS also claims that it is THEIR discretion, if they want to allow you to stay in US after those 240 days.
H4 dependents are allowed to stay beyond 240 days - real world
In real world, the H4 dependents are ALLOWED by USCIS even after 240 days (of i94 expiry) to stay in US, as long as their primary H1B’s visa is VALID.
USCIS processing time update
Unfortunately, USCIS does not reveal as to when they will process your application. You can just guess based on the current H4 processing time:
H4 USCIS case Inquiry if your case is pending for more than normal processing time
You can open a case Inquiry with USCIS to check why your case has been pending for such a long time, if it is past the date mentioned on above H4 Processing time page.
I strongly recommend to do case Inquiry in your scenario.