Headstones at Westburn Cemetery in Cambuslang are currently being inspected by council staff.
South Lanarkshire Council (SLC) has a duty of care to provide a safe environment for both visitors and staff.
Westburn is the latest plot to be inspected as part of checks being carried out at all 55 cemeteries across the area.
Around 25,000 headstones have been checked so far.
Fully-trained operatives carry out the checks, and where a headstone is found to be unsafe, lair owners are contacted in writing and a sign attached to the headstone advising issues with its stability.
If the headstone shows significant movement and is deemed unsafe, it is immediately secured by use of wooden posts and banding.
Advice is then given that the lair owner should contact the memorial mason who erected the headstone to look at the possibility of making a suitable repair.
The council's head of facilities, waste and grounds services, Alistair McKinnon, told Lanarkshire Live : “We do not have the right or the responsibility to make repairs to headstones.
“However, should the lair holder not make contact within the designated timescale, we will lay the headstone flat or ‘trench in’ the headstone to ensure safety.
“We acknowledge that in some cases families may be attending the lair without full knowledge of the process and we would apologise in advance for any distress caused.”
Information will be posted on the notice boards at the entrance to each cemetery when inspections are taking place.
Should you wish to discuss any matter arising please contact Bereavement Services by calling 0303 123 1016.
