This is not a big study, but its so important; these researchers in Japan showed that the strength of muscles in your torso was related to the strength of the muscles that help you swallow your food.
Now, swallowing is a very complex process, perhaps evidences by the fact that there is a whole profession dedicated to the study of speech and swallowing (speech pathology). Whether you are easily able to chew and swallow food depends on more than just muscle strength, but loss of muscle and poor muscle function is certainly part of the picture when people have to modify the texture of their meals in order to be able to eat them safely.
So, everything you can do to keep up strength in the muscles that help you get food from your lips, safely into your stomach, is valuable in allowing you to continue to enjoy the foods you like into your later years.
In later age many people can find themselves being recommended to some sort of texture modified diet - having to have foods minced or pureed/ blended in order to be able to eat them safely. There are lots of chefs in aged care now working hard to improve the quality of texture modified food and I applaud them, but its so much better if you can avoid needing to have the texture of your meals altered it in the first place.
I don't know about you, but I want to avoid having to eat puree every meal , no matter how well its made, in my later years if at all possible!
So here is an answer: do physical activity that requires the muscles in your trunk to stay strong. That's really anything that keeps you upright because your trunk muscles are the ones that hold your spine upright. You can also do abdominal strength work, but its enough to keep yourself doing plenty of activity that keeps you fighting gravity and standing as tall as possible.
So stay active and also get to keep enjoying food the way you like it best.