It is my understanding that the FPGA companies only manufacture the FPGA chips that take the VHDL or Verilog code to configure them to perform the programmed specific functionality. They do not take the design further. Many smaller start up groups will use the FPGA parts for proof of concept and proof of marketing plans. These parts are however quite expensive and are not priced competitively for most any type of production.
The design that is in the VHDL or Verilog code many times is sent to the vendor of the ASIC chip design house to be converted to the metalization layers for the sea of gates design. Some of these houses have their own chip fabrication facilities and others use commercial fabrication facilities that do nothing other than fabricate integrated circuits. Either way, the design that is contained in the VHDL or Verilog code eventually gets converted to the metalization layer patterns and those patterns get fabricated into a “custom” integrated circuit some times called an ASIC (Application Specific Integrated Circuit)
There are many such design houses that specialize in taking the code for various FPGA designs and turning that code into integrated circuits.
The above is only my opinion based on personal experience for what it’s worth.