Use Rubber Shelf Liner To Keep Tablecloths from Sliding

Table surfaces are slick, and keeping your tablecloth in position may require a grip pad in between the tabletop and the cloth. Using a rubber grip mat, such as shelf liner on tabletops will minimize movement by creating a little much needed friction.

These can not only minimize movement, but can also provide protection from hot plates and create padding to preserve the condition of the tabletop. 

Shelf liner is often used to create grip in a variety of situations to prevent unwanted sliding of all sorts of objects.

Several other uses for shelf liner

• Create grip for appliances on counter surfaces.
• Use under pet bowls to prevent them sliding across the floor during feeding.
• Place a piece next to front and back doors as it makes an excellent 'landing place' for dirty/wet shoes
• Place in between pot and pans, or fine china, to prevent scratching and dents
• Use it in the bathroom to prevent shampoo bottles from slipping of shelves, and also prevent these items from leaking onto bathroom surfaces and creating rust stains.
• Place some in your trunk to prevent items in your boot from moving around whilst cornering.
• Place a piece under a potted plant to prevent leaks and moisture from damaging decking

Basically, if you have an object on a slippery surface and you want to reduce its ability to move, then this stuff is great. It's also useful for protecting surfaces from spills and leaks as non adhesive liners are machine washable, meaning the liner can be re-used.

These aren't necessarily going to anchor your tablecloth but they'll contribute to minimizing the extent to which you tablecloth slips out of place.