This is a serious and potentially dangerous situation. It sounds like you've uncovered a real mess of improper and unsafe electrical work. Let's break down the problem and discuss potential solutions

Understanding the Problem
Severity

You've described a house with widespread, significant electrical deficiencies. This goes far beyond a simple "hairdryer tripping the breaker." Loose connections are a fire hazard, and bypassed AFCI protection leaves the occupants vulnerable to arc fault-related fires. The neutral/ground issues are equally concerning and create shock hazards.

Root Cause Speculation

It's likely that the original wiring was done by someone unqualified or extremely negligent. It's also possible that a series of different people have added to the problem over time.

AFCI Malfunction

The core of your immediate problem is that the AFCIs aren't tripping when they should. This defeats their purpose and leaves the circuit unprotected. The fact that they trip with the test button indicates the breaker itself is functional to some extent, but the arc fault detection circuitry is not responding as expected.

Possible Causes for AFCI Failure to Trip with N-G Fault1. Incorrect Wiring (Even After Your Corrections)

Neutral-Ground Bond Issue: Double-check, and then triple-check, that the neutral is only bonded to ground

at the main service panel. If there's a neutral-ground bond anywhere else in the system (like in a subpanel or even at a receptacle), it will defeat the AFCI's ability to detect ground faults. AFCI's work by measuring the current difference between the hot and neutral. If there's a parallel path for the neutral current to return (through an unintended N-G bond), the AFCI won't see the imbalance. This is the most likely culprit. Shared Neutral Issues: Make sure no circuits are sharing a neutral, especially circuits protected by different AFCI breakers. This will cause erroneous readings and trip the breakers. Neutrals Landed on the Wrong Bar: While you've corrected the pigtail issue, ensure the neutrals for each AFCI-protected circuit are landed on the correct neutral bar and that there's no chance of neutral cross-wiring between circuits. Loose Neutral Connections: Even though you've addressed loose connections, ensure that the neutral connections in the panel are tight and secure, as any resistance in the neutral path can impact the AFCI's sensitivity.2. Damaged AFCI Breakers

Abuse or Overheating: Given the initial state of the electrical system, it's possible that the AFCIs were damaged before you corrected the wiring. They may have been subjected to surges, overloads, or overheating due to the faulty connections. Hidden Damage: There's a chance that the tampering with the pigtails could have caused internal damage to the breaker's electronics that isn't immediately obvious.3.

Circuit Load/Leakage

Excessive Leakage Current: While less likely, a high level of leakage current on the circuit could "mask" the additional current from a ground fault. Appliances with filters (like some TVs, computers, and some LED lighting) can contribute to leakage. Try isolating circuits by turning off breakers to appliances and see if that helps.4.

Defective AFCI Breakers

Manufacturing Defect: It's always possible that some of the AFCIs are simply defective from the factory.5.

Neutral Current Imbalance from Other Circuits

If you can measure the current on the neutral of the circuit with an ammeter, you may be able to see an imbalance of current between the hot and neutral even without creating a fault. This imbalance can cause the AFCI to not trip with an artificial fault.

Troubleshooting Steps1. Systematic Inspection

You need to approach this methodically: Document Everything: Before you change anything else, carefully document which AFCI breakers feed which circuits. Label everything clearly. Neutral-Ground Bond Verification: This is CRITICAL. With the power off, use an ohmmeter to verify that there is NO continuity between the neutral conductor and the ground conductor except at the main service panel. Test this at multiple points in the house (receptacles, light fixtures, etc.). Isolate Circuits: One at a time, turn off all breakers except for one AFCI breaker you want to test. Disconnect any appliances or devices plugged into that circuit. Then, perform the neutral-to-ground fault test. If it trips, the problem might be with other circuits interfering.2.

AFCI Testing & Replacement

Individual AFCI Test: After verifying wiring, replace one AFCI breaker with a

known good AFCI of the same type. Perform the N-G fault test. If it works, the old breaker was likely faulty. Manufacturer Support: If you're still having problems, contact the AFCI breaker manufacturer's technical support. They may have specific troubleshooting steps or be aware of common issues with their product.3. Professional Consultation

Independent Inspection: Strongly recommend to the customer that they have an independent electrical inspection performed by a qualified, licensed electrician who is experienced with AFCI systems. This will provide an unbiased assessment of the entire electrical system.

Important Considerations Safety First

Always work with the power off when troubleshooting electrical wiring. Wear appropriate PPE (safety glasses, gloves).

Documentation

Keep detailed records of everything you do, including your findings, the tests you perform, and any corrections you make.

Liability

You are taking on significant liability by working on this system. Make sure your insurance coverage is adequate. The customer and contractor need to understand the severity of the issues and the potential consequences.

Permitting

Depending on your location and the extent of the work you're doing, you may need to obtain electrical permits. This can also trigger inspections that can help ensure the safety and compliance of the electrical system.*

Do Not Cut Corners

Don't be tempted to "work around" the AFCI issue. These devices are there for a reason, and bypassing them is dangerous and illegal.

Recommendation

Given the extent of the problems you've found, the best course of action is a complete electrical system inspection and, potentially, a partial or full rewire. This is a serious situation that requires a comprehensive solution. I would advise you to fully document your findings, explain the risks to the customer and contractor, and recommend they hire a qualified electrician with extensive experience in troubleshooting and correcting electrical code violations.This is not a situation to take lightly. Your diligence in uncovering these issues has potentially prevented a fire or other electrical hazard. Flag for review