This one is real, it happened to me a few months ago (February 2020 in Cogne, Italian Alps, just on the Italian side of the Mont Blanc Tunnel).
Ice climbing day. I led a 40m pitch of WI5 and I was unable to find the fixed anchors of the belay station (bolts on rocks usually, or the ocassional sling arround a tree). I guess it was either buried under the snow (lot's of snow this year). I found the remains of an old belay station (just the metal inserts in the rock but no bolts or rings or anything).
I installed an ice screw, anchored myself and proceeded to creat a V thread anchor (also called avalakov). For those not familiar with what a Vthread is I will explain. You take the longest screw on your rack (usually 22cm) and insert it in the ice sideways at an angle (45º or so), then you remove it and inser it again from the opposite side trying to get the previous hole and this one to connect. You creat a V shaped tunnel in the ice.
Once you have the tunnel made, you thread a piece of cord through it with the help of a hook, tie it off and cut the excess.
And then is when things got funny because... I was not wearing my regular climbing pants and I realised after tying off that... I had left my Spyderco Rescue in the backpocket of my other climbing pants in the car.
What should have been a quick slice with a sharp knife become a real long struggle to cut the 8mm cord with the sole aid of my ice tools. I planted one of them firmly on the ice, used the hammer on the back of the had as an anvil and banged on it with the hammer of my other tool. Eventually I chopped it off. In turn this situation gave me confidence that it is not that easy AT ALL to cut a climbing rope against a rock during a fall.
Not a life or death situation because I only had to abseil to the ground and I could have left the whole 5m long coil of cord up there and be done. But had it been a multipitch abseil on avalakovs.... I whould have meant trouble.
So, two things to remember: MAKE SURE YOU HAVE YOUR KNIFE ON YOU and BUY A NEW VTHREAD TOOL THAT INCORPORATES A BLADE AND THE HOOK IN THE SAME TOOL!!!!
Mikel