Denial based on failure to complete conversion paperwork

Hi all, apologize in advance for the long post…this is my first time posting on reddit (out of desperation, I suppose), but want to include all relevant details. I know it’s a long shot but grasping at straws here, hopefully someone has some hope for my family. My mother recently passed away after a 12-year battle with cancer. She’d always had Hartford life insurance through her employer, then unfortunately had to move to short-term disability, long-term disability, then ultimately retirement as her health deteriorated and she spent more time in/out of hospitals. She felt strongly about having life insurance so even after her passing, she’d still be able to help take care of her children and husband in some way. Imagine our surprise when we called after her death and were told there was no payout, because somewhere during during the transition from employed to retirement, there was a conversion form of some sort that had to be completed that apparently never was ( though as far as I know she was still sending payments somewhere). The life insurance company claims they sent 3 separate copies of this form to her informing her that she needed to convert the policy, but only through regular USPS mail (not certified mail, no proof of delivery, etc.). I never saw or heard her mention receiving this form (though I helped her manage many things as she got sicker), and in addition, she lived in a small country town where occasionally mail didnt always make its way to the correct recipient. I’m just having a really hard time wrapping my head around her just choosing not to do whatever needed to be done to keep her life insurance, as she knew the end was approaching. I don’t know that she ever did receive these forms, or if it was delivered, was it while she was in the hospital fighting for her life and unable to handle those affairs? There was mention at one point (I think from a rep my brother spoke with) about being able to prove that she was in medical crisis at the time when this conversion process was supposed to have taken place, but not sure what that would look like or even if that’s helpful. The rep I spoke to was fairly unhelpful and unsympathetic to our situation.
I’m not sure there’s any recourse for us, or any legal route to avoid just shrugging away hundreds of thousands that my mom had counted on leaving to help care for my dad, based on a piece of paper not being signed.

Any help or insight is very much appreciated.