Identify Warning Signs

• Check if the Check Engine Light is illuminated.
• Listen for unusual noises from the engine or any misfiring.
• Notice any unusual behavior while idling, such as rough idling or fluctuating RPMs.

Check the Fuel System

• Fuel Filter: Ensure the fuel filter is not clogged. A dirty filter can restrict fuel flow and cause stalling.
• Fuel Pump: Test the fuel pump for adequate pressure and proper functioning.
• Fuel Injectors: Verify that the fuel injectors are clean and operating correctly. Cleaning or replacing them might be necessary if they are clogged.

Inspect the Air Intake System

• Air Filter: Check if the air filter is clean. A dirty or clogged air filter can cause poor air flow, leading to engine stalling.
• Mass Air Flow Sensor (MAF): Clean the MAF sensor to ensure it's providing accurate readings to the ECU. A faulty MAF sensor can cause incorrect air-fuel ratios.

Evaluate the Ignition System

• Spark Plugs: Inspect spark plugs for wear and tear. Replace them if they appear worn or dirty.
• Ignition Coils/Wires: Make sure the ignition coils and wires are in good condition. Faulty ignition components can affect engine performance and lead to stalling.

Test the Battery and Charging System

• Battery Condition: Check the battery terminals and cables for corrosion and secure connections. A weak battery or bad connection can cause engine stalling.
• Alternator: Verify that the alternator is functioning properly to ensure the battery stays charged.

Examine the Vacuum System

• Check for vacuum leaks in hoses or connections. Leaks can disrupt the air-fuel mixture and cause engine stalling.

Inspect the Electronic Control Unit (ECU)

• Trouble Codes: Use an OBD-II scanner to check for any trouble codes that could pinpoint an engine issue.
• Reflash or Update: If the ECU software is outdated, consider reflashing or updating it at a Toyota service center.

Regular Maintenance

• Keep the vehicle well-maintained with regular oil changes and scheduled services.
• Ensure all fluids are at appropriate levels and are of good quality, as specified in the owner's manual.

By systematically checking these areas, you will be able to identify and resolve the issue causing engine stalling in your 2005–2007 Toyota Corolla. If you are unable to diagnose or fix the problem, it is advisable to consult with a professional mechanic for further assistance.