I'm thinking from your name you're female...??
Try tucking the other headphone in your bra..that's what I do. Or, use a safety pin to pin it on the inside of your shirt.
I've noticed that if I keep my music at a fairly low volume - probably lower than if I used it for other recreation - I can hear vehicles, people, and other random sounds just fine.
I encourage everyone to do this, one headphone or two, for the greatly reduced chance of hearing loss, as well as for being aware of surroundings.
When I run I only use one headphone and I tuck the other through my headband. So its not bouncing around and has the support to not pull out my other one. So far it works.
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