@bunny123 I missed appointment once due to emergency situation. I contacted USCIS office via phone. They asked to send a letter explaining the reason along with appointment copy.
Usually it takes less than 30 days to change the USCIS appointment but it may vary depending on the center and workload.
@enterpreneur I think your friend is in a very sticky situation! Ask your friend to contact an Immigration attorney ASAP.
Technically a person can stay in US while their H4 petition is pending adjudication up to 240 days after expiry and if they have been working or running a business they should stop working at the date of their EAD expired.
Regarding the business, they could assign a legal power of attorney who is eligible to run a business here to handle business dealings while they are out the status. Again these things involve detailed analysis, please check with your immigration attorney immediately.