Can an ex-husband take out a life insurance policy on ex-wife?

If she is agreeable to it. The insured typically has to sign the application and undergo a physical, it isn't something that can be done in secret. And if there are children involved there is certainly a reason to do so.
If she is agreeable to it. The insured typically has to sign the application and undergo a physical, it isn't something that can be done in secret. And if there are children involved there is certainly a reason to do so.