How do I stop my expensive mattress from sliding off the matching box

Get some of the rubber type rug stuff that stops the rugs from sliding on the floor. Put it between the mattress and box springs.

Try putting a bed skirt on, it has that fabric between the mattress an box spring that might help to stop sliding.

The standard fix is to buy a non-slip rubber pad made for area rugs. You should be able to find pads at any store that sells area rugs. The most common area rug sizes that you might need are 3'x5', 5'x8', or 6'x9'. The pads will be slightly smaller than the rug they are made for. The 3x5 will work for a twin and you can use two of them for a king. You can also use a single 6x9 for a king, but you need to cut off the excess length. The 5x8 will work best for full and queen sizes, but will also need to be trimmed.

I would try the pad before cutting it to make sure it doesn't slip. Remove the mattress. Lay the pad over the box springs and replace the mattress. Sit and lay on the mattress. Get on and off the bed as you normally would several times, because this movement is most likely to cause slippage. If you are satisfied, remove the mattress and cut the pad down to size. If you are not satisfied, repackage the pad and return it to the store. Look for a different type of pad. They are made of urethane foam, felt, rubber and combinations of these.

I've used Velcro strips in the past.

Purchase a box spring coverwhich encases entire box spring. The fabric will provide friction to preclude movement of mattress.