We eat a lot of chicken I keep cooked shredded chicken breast in my fridge almost all the time. I buy boneless skinless on sale I simmer them with onion, garlic, celery, all the usual suspects. When done I cool and shred it with a fork. Great for topping salads, or eating with cheese and fruit or making burrito or taco bowls. I save the cooking liquid to make a varriety of chicken soups with the whatever fresh or frozen vegetables I have leaving out the high carb starches. You can also use whole chicken it's just more work to defat the broth when you want to use it.
This can also be done with a pot roast I throw a giant one in the crock pot with the onions celery carrots garlic rosemary what ever floats your boat and beef broth Cook till it falls apart shredd and use the same as above.
I don't know how no or low carb you are trying for but there are some breads and wraps available that are not bad and work for when you really want it in a sandwich.
We don't do no carb we just try to get 75% of our carbs from unprocessed sources like fruits and vegetables and keep the breads, pastas, and white or processed rice to a minimum.