I saw a Scheme interpreter written in assembly running a C compiler written in Scheme.
There’s actually good reasons for this design. It’s easy to write a Scheme interpreter in assembly, but it’s hard to write a C compiler in assembly that handles everything correctly. Much rather write it in higher level language if possible and Scheme lowers the bar to getting there, so you can get away from using assembly as quickly as possible. Or you can copy somebody else’s Scheme implementation of a C compiler because now you’re platform independent.
Then you can write your C compiler in C (or steal a better compiler already written in C) and close the loop. For your final step, you use the C compiler to compile itself.