I'm Lucy, and I'd be happy to answer your questions today.
Adverse possession requires that a person use the land of others, without consent, continuously and in a manner hostile to the true owner, for many years. In the context of a grave site, that's not a concept that would come into play unless the husband was interred without the consent of the property owner, and it doesn't sound like that's the case. The wife had permission to put her name on the gravestone, and she's not physically occupying the space yet, so she has no basis for claiming adverse possession. If the wife paid for a double headstone and for a grave that she and her husband would share, then she has a right to that property under general contract laws. All she (or her next of kin) needs to do is see if she can find the original paperwork showing that she paid for the site.
There shouldn't be any basis for refusing the wife access to a burial site that was long since paid for. If the cemetery will not inter her, they could be held responsible for the costs of finding another location. The wife (if she is still alive) or her estate could actually sue the burial ground. Usually, court is for making someone whole by paying them monetary damages. However, specific performance is allowed in some cases where money damages simply cannot repair the damage to the injured party. So the wife could argue that money is not an adequate substitute for spending eternity next to her husband, and it's possible a judge could order the graveyard to comply with the contract. The cemetery districts were created to provide for maintenance. I'm not finding anything that says changing districts invalidates existing contracts (and there could be a constitutional argument that the law interferes with the right to contract if it did say that).
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