How can I stop my pillow from falling off a border-less mattress?

You say you the bed is used in its flat position.

Solution 1 –

Position the head of the bed against a wall or an item of furniture, so that the pillow does not slide off.

From the photo it looks as though there is room to turn the bed by 90 degrees and use the wall. If not, remove the clutter in the corner behind the bed.

Solution 2 –

Sleep the other way round, so that the metal hoop at the 'foot' can retain the pillow.

If that isn't enough support, stand a sheet of MDF at that end, drill some holes, and use plastic ties to secure it to the metal hoop and the legs. You now have a makeshift headboard.

I can think of a few options:

• Fit a headboard of their own choosing

• It should be relatively easy to sew a couple of bands of elastic onto a pillow case so that the elastic goes around the mattress. If you're having trouble envisaging what I mean, think about a watch with an elasticated strap. The strap hugs your wrist, and the face protrudes. In the same way the elastic hugs the mattress and the pillow in its case protrudes

• Consider sewing the pillow case to the bed sheet, if they don't want to change the aesthetic of their sheet/case color matching regularly

• If their sewing skills aren't up to this and nowhere locally can help, consider taking a pillow case and make two cuts in the bottom (the bit that touches the mattress when it's in sleeping position) near the closed end. Thread a belt, rope, strap or similar fastening into the open end of the pillow case and out through each hole and then flip the whole lot over and strap the pillowcase to the bed, then fill with a pillow

• perhaps the simplest solution, if they want to go for it, would be to put the bedsheet over the top of the pillow when making the bed

Cut a pool noodle in half lengthwise and put it under the fitted sheet at the top of the bed. Easy Peasy. No more pillows falling off the bed.

For about $20 you could get an anti-slip cushion gripper (like this or this). These mats are basically a smaller, softer version of an anti-slip mat cushion for a rug. If you cut a strip the width of the bed that the depth of the pillow then you could probably keep a pillow sitting on the mat from sliding around or off the bed. They work by increasing the friction between the sheet and the pillow case.

Another possibility it to get a very heavy pillow. For example, the Purple Pillow weighs 10 pounds and likely isn't going to budge. More conventionally, a traditional memory foam pillow in king size weighs about 4 pounds. In contrast, a standard size down pillow weighs about 14 ounces.

Upholstery twist pins work like a charm for this and they’re super cheap, about $5. https://a.co/d/07smiC4f