Cemeteries have some real ongoing maintenance fees — mowing is among the largest, but there are others, such as downed tree removal, snow removal, and administrative personnel. Additionally, some countries mandate that burial plots be maintained indefinitely (United States is one of these).
To fund this ongoing maintenance, a perpetual care fund/perpetuity fund is established. [1] [2]
Sometimes a cemetery becomes abandoned or severely unmaintained, sometimes because of lack of funds to maintain it. In some of these situations, someone else will take over maintenance, perhaps the town/county it's in, perhaps a nearby church, or volunteers. [1] [2]
Some groups have their cemeteries less respected, including African-Americans [1] [2] and Native Americans [3].