A simple way to view this is any excessive stress makes a person more susceptible to well, basically you name the ailment. (For an extensive look at this, see Robert Sapolsky's Why Zebras Don't Get Ulcers.)
In which case, you can overtrain from any activity. Even if your job involves you sitting down all day, if it's significantly psychologically taxing you, that will eventually lead to overworked aka overtrained. That is, overtraining isn't only a local phenomenon, such as muscles. It can be a central one i.e. the nervous system.
Another example would be chess players. Just because they're not moving doesn't mean their cardviovascular system isn't in overdrive. Or, if you're into video games, you've experienced your heart racing despite barely moving. In other words, just sitting down, if stressed, gets the blood flowing. Chronically doing that will have negative consequences, eventually impacting your ability run.
If work is kicking your ass for 12 hours every day, your training, whether lifting, running, or badminton, isn't going to go well. This is a major reason professional athletes don't do anything besides their sport.***
More specifically, runners are notorious for upper respiratory infections. Just Google "long distance runners upper respiratory infection" and you'll have plenty to keep you busy for a while.
But really, one should view this more broadly as, to some degree, stress is stress. For instance, a lack of sleep impacts everything. If the nervous system is worn out, nothing functions as well.
***During a division I football season it's been found the players are more likely to get hurt during academic test periods. Their muscles aren't more stressed during those periods, but their brain is.
Also, med school students are more likely to get sick during test times, because they're so stressed. Any wounds they have will heal more slowly too!