Can a life insurance policy be purchased on an individual without their knowledge or consent?

I am so sorry for your situation. You need to take your divorce agreement to an attorney to review as soon as you possibly can.  It should have been part and parcel of the divorce that he keep a life insurance policy for the benefit of your children should he pass away unexpectedly.  AS to what is says and what you can do now, you are limited.  You can not take out a life insurance policy on your ex husband.  You do not have what is known as an insurable interest in his life. But if he was to have one in effect for the kids and thee is not one in place but rather another policy around, you may be able to claim it for the kids.  That really depends on case law in your state.  Such an exception will only be carved out there.  You are really enforcing the agreement.  It may seem cruel at this stage but you need to go against the estate for the benefit of his kids. Get help.  Good luck.