I have a favorite pair of fuzzy Dearfoam slippers given to me several years ago that are made with a cloth sole. I have worn through the soles, but haven't figured out what to use to adhere to these cloth soles to allow for more wear.
This can be done but, as stated, be sure you also do something to make the slippers NOT slippery.
Here is a site that does show how to do this (and it can be done) but you may want to check out different types/thicknesses of felt at a craft or sewing store.
Here is a link with suggestions about how to make your slippers safe.
You could probably iron on a patch. However, my experience has shown that worn out soles are slippery and dangerous. You might want to invest in another pair.
A while ago, I got desperate and repaired mine with a bit of epoxy and patchwork, but like Judy says, it became very dangerous. I hurt my ankle. I wouldn't suggest patching things like shoes.
I never replaced slipper soles before and I understand the pair you have had for several years, but for your new pair/heads up as a reference they have 1 year warranty: www.dearfoams.com/warranty.html
You could maybe try a foam supplier that does custom cut foam? Like this one - www.foamdirect.co.uk/