I think the small freezer on their main floor is a good idea. However, the thought crossed my mind.... how easy is it going to be for your parents to open the chest freezer, bend over and get what they need/want, especially if the item is in the bottom of the freezer?  This is something you might want to look into before purchasing.  I don't know if small upright freezers are available. If so, maybe an upright freezer is a better idea for your parents, just for the convenience of use.  Just something to think about.

An idea that has crossed my mind, but I have never implemented.... fill containers with water, and place them in the bottom of the freezer.  These would take up space, hold "cold", and never be used. They would help keep food items nearer the top of the freezer so it is not so difficult to bend over and reach into the bottom of a chest freezer. It might be a low-cost idea to use, that would be worthwhile in some situations. Maybe like for your parents.