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yes. A joint tenancy is a joint tenancy until such time the joint tenancy is dissolved. If it was a joint tenancy, the ownership immediately and fully becomes the property of the remaining joint tenant(s) upon the death of any of the joint tenants. Probate does not have any control over the transfer of the property. It cannot even be willed to others. It simple is owned by the remaining joint tenant(s).
well, if it can be determined the probate action was incorrect, the transfer can be reversed and the entire property is open to attachment.
If the state takes action prior to her death, that action can be continued against her estate. If they do not take action prior to her death and your joint tenancy is legit and there has been no fraud or deception in achieving the benefits, once she dies the real estate is no longer part of her estate and no longer able to be taken.
Now, MO does have what is called a tenancy in the entirety that is available only to married couples. If that was the case, I am not positive, and would have to do some research to find out, but that may revert to a tenancy in common upon the dissolution of the marriage. If it had, then your fathers share would be controlled by the laws of probate.
But any parties (basically) can enter into a joint tenancy so it would not be affected by the divorce. Now, there could have been a court order that was followed the parties dissolve the joint tenancy but that does not sound like what happened.