Anything above "moderate" weight or exertion and we run a risk. Give players a strength/stamina related fall chance. Give sheet ropes a durability, reduce by use as defined by X (Thus 3 height at 40 weight = 12 durability per climb.) and if it reaches zero at any point during your climb, your fall is calculated from that height. Real world application though there's NO reason you couldn't knock out the stairs and live on the 2nd floor of a building other than the potential for injury preventing you from climbing.
To add to the confusion, if you FOUND a ladder and laid it against the wall to climb, zombies could always knock it over, meaning you'd be stranded up top. This way the sheet ropes are still last resorts, if you're exhausted you can still climb down, but for a permanent fixture you need to add more commitment to it. I don't like the thought of zombies ripping the rope, I think simply adding more tedium to it would be enough incentive to use the more dangerous but long term alternative, at least until higher levels of carpentry to make ladders. Regular ropes would be much more robust and ladders would be permanent until destroyed manually. What could also work pretty well is to give each rope a Condition stat, like the weapons, and each climb has a chance to degrade the quality until it breaks.
Adding zombies destroying the rope would only overcomplicate things, though I do agree you should be able to use a regular rope for a more sturdy long term climbing. As much as I love the brainstorming, I do think that the addition of moodle based climbing alone would do the trick.