Depending on your exact model of Kenmore side by side refrigerator, the following issues could cause freezing in the bottom vegetable bin:
Blocked or improper air flow through the refrigerator section
Failed air damper (stuck open) or a control failure
Failed sensor or thermostat
Defective electronic control board (if present in your model)
Here are some general tips that may help you resolve this problem:
Make sure that the incoming cold air damper vent at the top left side of the refrigerator is not blocked.
Make sure that the return air vent at the bottom left side of the refrigerator is not blocked.
Do not overload the refrigerator so that air flow is blocked.
If you have a separate air vent for the meat pan, you may need to close this vent or block it off.
Try adjusting the refrigerator temperature to a slightly warmer setting and the freezer to a slightly colder setting to increase fan run time and circulate the air more consistently inside the refrigerator.
Check the refrigerator and freezer door seals for cracks or loose spots.
If you need more help, resubmit your question with the full model number of your Kenmore side by side refrigerator.