Life insurance post-sep and divorce

Clarifying a prior question (thanks)-- once any dependents have aged out/ moved out, can I be required to carry life insurance if ex is the sole beneficiary-- What if spouse is considered dependent (is awarded alimony)-- could I then be compelled to carry life insurance (it will get much more expensive at renewal due to health problems having developed since last applied for)-- if so, for how long?

                                                                                                                                   Thank you

Typically no, but in some cases life insurance can be required in special cases for so long as you have a support obligation.