Can GDB change the assembly code of a running program?

You can write binary to memory directly but GDB doesn't have an assembler build in by default you can however do something like set *(unsigned char*)0x80FFDDEE = 0x90 to change the mnemonic at that address to a NOP for example. You could however use NASM to write a shellcode and use perl or python to inject it into the program :)

You might also like this little .gdbinit file to make debugging allot easier: https://gist.github.com/985474

I would recommend a different approach: Download the coreutils package and modify the source code for ls. If possible, you should get the package from your distro's source repositories and apply any patches.