The core method of dealing with a faucet broken inside a water pipe is to remove the stump using specialized tools or sawing. The most common and efficient solutions include wire break extractors, hacksaw cutting and welding assistance, depending on the location of the break and tool availability. 

Commonly used methods

Wire Extractor Method (Recommended)

Purchase and broken wire caliber matching the broken wire remover, screw it clockwise into the stump inside, the use of reverse threading principle of clamping and then rotate counterclockwise, you can bring out the stump. 

Advantage: simple and fast operation, no damage to the internal threads of the water pipe, suitable for family self-operation.
Hacksaw cutting method.

Use a fine-toothed hacksaw blade to saw the stump longitudinally out of two symmetrical cuts (depth to the internal thread layer of the water pipe can be), and then use a flat screwdriver to pry out the debris from the cuts. Note: Avoid sawing too deeply to cause water leakage of the water pipe, and keep the saw blade parallel to the axis of the water pipe during operation.
Welding assistance method.

If the exposed part of the stump is long, you can weld a metal bar or nut on the fracture and remove it with the help of a wrench by turning it counterclockwise. 

Applicable scenario: only applicable to the case where the break is exposed and welding conditions are available.
Key steps before operation

Turn off the water source: Be sure to close the main valve to avoid spraying water during operation. 

Prepare tools: Prepare tools (e.g. wire break extractor, hacksaw, wrench, etc.) according to the chosen method. 

Cautions and alternatives

If the stump is completely embedded in the wall piping and cannot be removed, the original tee pipe needs to be melted down and replaced with a new part at a cost of about 100 RMB. 

The old zinc alloy faucet is easy to break, it is recommended to replace the faucet with an all-copper faucet to enhance durability. How to get out the inside part of the broken faucet