Our terrible health insurance situation makes potential spending any given month very bumpy. $10k should be enough to keep a single, frugal person in an OK situ

Our terrible health insurance situation makes potential spending any given month very bumpy. $10k should be enough to keep a single, frugal person in an OK situation for a good chunk of a year, at least, but could just as well be blown inside 24hrs by one slip on some ice or any number of other ER-worthy problems, and isn't enough to cover a healthcare plan that removes much of that uncertainty for any length of time while also paying rent and buying food.