How do they construct subway tunnels?
All subway systems have tracks that come to the surface and have yards for repair and storage of extra cars. Subways are expensive and where possible the actual running lines are on the surface or actually raised above the ground, so switching to the yard is simple. Subway tunnels are made either by cutting a trench in the ground, putting concrete into it either as preassembed pieces or by pouring, the covering it over (as done in San Francisco and parts of Washington DC) or using the huge boring machine you describe in which case there is a metal shield that holds up the roof at the cutting edge and concrete is injected behind it and sets as the machine is pushed forward so when the machine advances it leaves the structural concrete behind. Normally this is top coated and painted for better appearance. If the boring is through good rock, concrete may not be required.