Absolutely correct.You might be surprised.
If the place get's mowed, there is a group that manages it. If they are still planting folks there, someone is opening the graves.
My family is mostly all buried in a small cemetery, in a small Western OK town, and there is a local committee of citizens that look after it. There is a president, a VP etc etc. I've had several relatives that live there that have been various officers for the cemetery committee. They know everything there is to know about that place.
I really hope you get it fixed to your satisfaction. I go a couple times a year to check on my dad & sister's stones to make sure they aren't sinking, or the vases haven't cracked or come loose. I spread a little ant bait around, take a wisk broom to everything and I'll Windex the polished side of the stones. I know they don't care, but it makes me feel better. I get a letter a couple times a year with the financials of the place, and a list of recent burials. One of my dad's vases popped loose a year or so ago, and the guy that mows picked it up and took it to my cousin's house. He kept it for me until I could get out there to get it reattached to the stone.
If the place isn't overgrown and completely wild, they might not have any "employees" but I'd bet there is someone or a committee that looks after the place. You might ask around at the co-op or grocery store if there is one there. A close funeral home would probably know who to contact as well.
Best of luck to you, and bless you for looking after your relative's marker.
We have relatives in small rural cemeteries. Really small. I see them slightly overgrown occasionally, but around memorial day, they are all mowed and weed eated. We pay a small amount to the cemetery fund annually.
We do have abandoned cemeteries in the same area as well that get no maintenance. Lots of trees growing up around the graves, etc.