Can a spouse cancel your health insurance before the divorce?

I believe you are both responsible for any bills incurred (such as health care costs) until you are divorced, so in some cases it would behoove a spouse to keep coverage on the other spouse so that they don't end up responsible for a large bill in the case of an accident or serious illness. However, if there is a separation agreement with a clause about neither party being responsible for any debts incurred after the signing of the agreement, one may be able to drop their spouse from insurance without issue.