April, After seeing a similar question about sheets to big for short mattress, I realized I've got the same problem with the mattresses for a bunk bed just delivered for my granddaughter.
My challenge is compounded by difficulty reaching all 4 corners of each bed so what I'm going to do is sew elastic bands on each sheet corner. I expect to sew them 6 to 8 (maybe a bit longer) inches from the corner to make it easier to slip the bands over the corner of the mattress when I'm leaning over the bed ... only access to one side of bunk beds.
This is similar to how mattress pads and today's mattress toppers do it, so I'll probably try to find one of these to confirm where bands should go.
I use the Threshold sheets from Target. They wrap completely under the mattress and are impossible to slide off.
The only way is to fix it with elastic clips for the purpose available online, or like me change back to flat sheets.....
Large binder clips work well😊
I use the corner suspenders.... https://www.amazon.com/s?k=sheet+suspenders&crid=2YQ3A6X6VOTU7&sprefix=sheet+suspenders%2Caps%2C230&ref=nb_sb_ss_i_1_16