Can you run UNIX on PIC32 with onlt 128KB of RAM? Yes absolutely! Serge Vakulenko proves this with his RetroBSD port for PIC32 (MIPS).
The project is hosted at http://retrobsd.org/
Serge did amazing job by porting the old days 2.11BSD Unix used to run on PDP-11 to PIC32 (MIPS). In just 128KB RAM footprint he manage to boot UNIX OS and you have 96KB left for applications.
RetroBSD is multi tasking and you have access to the PIC32 GPIO and ADCs via API, so you can write embedded applications on it!