Can heavy, long endured stress cause the body to start shutting down?

Yes: Not sure what shutting down of the body is referred to, but long endured stress can definitely tell negatively both upon the physical and mental health being of the stressed one.

If shutting down is: Physical functions becoming altered then the answer is yes. Stress can alter function in almost every system in our body over time. Sleep and appetite are major areas, as well as cardiovascular health, muscle strength and stamina and how our endocrine system functions. Our mind can be affected significantly, altering how we learn, work, enjoy things and behave. We become accident prone as well.