You should first consider applying for a visitor visa extension if you can document the emergency. USCIS may approve an extension if the reason is credible and temporary. The application must be filed before your current visa expires.

If an extension is not possible, you should speak with an immigration attorney immediately. There may be limited humanitarian or discretionary options depending on your situation. Staying without approval can seriously affect future U.S. visa eligibility.

If no legal option exists, departing the U.S. on time is usually the safest choice. Leaving properly preserves your ability to return legally in the future.