the soil and cause the foundation to settle in the void and fall. Normally, water leaks like this are covered by insurance. But, before any work is done, the insurance company needs to know about it and they will send out their own plumber for a look see.
What will need to be done is to dig under the garage foundation and tunnel to the broken pipe. Fix the pipe and hopefully use pvc this time. then back fill the hole with packed sand. This will support the foundation to an extent. If you want the garage raised, then jacks will be needed and that could also be covered by insurance.
Normally a jack is needed every 8 to 10 feet. Jacks usually costs about $500 in labor and material per jack. This could be very expensive. You might want to just let it ride.
Now there is a chemical that I forgot the name that is used in the oil industry to support things in this situation. You pack it in with the sand and when wet it swells up big time and further supports the foundation.
I would document the situation, take pictures, and not let the city mess with the problem. They are careless and actually could care less, if its like our city.