I get a load of really horrid ones from the old bedridden guy I look after and I've never found any trace of them when I dig out the humanure heap.
I suspect there *may* be a few 'ultra tough' types that use a super-fine plastic mesh so they hold together better, so I make sure I always buy the cheapest, preferably unbleached and recycled, bog-standard tissues I can find. I guess if you're not sure, try soaking them in water till they fall apart and see if there are any threads that don't want to dissolve into mush.
I also use those moist toilet-wipes on the old man (I feel a bit guilty because it seems so wasteful, but I'm not going to accept cricisism from anyone unless they too spend far too much time handling someone else's poop) and so long as I buy 'flushable' ones they seem to disappear without trace.
I would also love to suggest something like my wife and I did to cut down on the waste portion. We have / had a front loading washing machine so I'm not sure how it works with top loaders as I don't like to use them and find they work poorly. Anyhow, my wife had a habbit of using about 12" plus of toilet tissue. When we started doing cloth diapers we changed to using cotton wipes, which she cut into about 6 x 6" or 8 x 8" squares of white cotton material. She uses these for urine only and still uses tissue for feces. This has cut down our use of toilet paper immensly and save money, you may or may not want to try this and see if it works for you. I love it and love the wipes. I personally am a little rougher round the edges and have no problem just using kitchen towel select a size for my feces wiping bit too abrasive for some