I know this is going to go against most peoples answers here but
Holding a Rope while someone climbs up it
Search Body Belay, i have done this while trad climbing and although this is uncomfortable, it is possible, don't let anyone tell you its not possible. if it were just about holding it with your hands then it becomes a lot harder, but by using a body belay then its definitely possible. it involves wrapping the rope around the body and over an arm. with this method it is possible to hold someone heavier than yourself, and if done right, hold them with one hand, again it is uncomfortable and requires you to be very sure footed but its still ok.
This is ok because it is a static load, while the act of climbing will create a few extra Newtons of force, it is still considered Static, now if that person was to fall on that rope, then not only would that rip the rope from the holders hands but most likely snap the spine of the faller.
Conclusion: Not comfortable, but definitely doable
Ground Anchor (sword)
Alpine Climbers regularly will place an ice-axe into compacted snow, and use that as part of their anchor, it is entirely possible to have this as the only anchor, although this is not advised only because if it was to fail then there is no backup
My Local Cliff Rescue team will regularly hammer stakes in a staggered pattern to use as an anchor if the ground is not solid enough on the cliff edge to set up a regular anchor, again this is done for redundancy, and conventional anchors are built whenever possible, but ground stakes are a suitable backup, and therefore they train on these often.
The only risk is that the sword will bend or snap due to the weight pulling in a way that a sword is not designed to do, the sword would have its blade edge perpendicular to the direction of pull, and angled away from the edge, then the rope tied to the handle. also it would have to be force DEEP into the ground
Conclusion: risky as no backup, but again doable, if there are no other alternatives
I have seen and used both of these methods, a lot of the world only does Sport Climbing so things like this are considered an absolute no, but Trad (traditional) climbers will do things like this.
Although i will state that Sport Climbers consider Trad Climbers to be a bit mental
As to how the enough time argument: how did the guy end up at the bottom of the rope, if there was a fight before hand that led to the the fall, then simply invent someway that a decent sword is already in the ground, maybe the wielder missed a strike, ended up stabbing the ground and then an attacker with a war hammer missed the guy and hit the sword on the pommel miraculously stabbing it further into the ground at the right angle, therefore its already there, the wielder might even make a point of trying to grab it but realizes its completely stuck, it seems not important and the reader will think wow now he has to fight with only a dagger, or fists or something, then it becomes an important plot point later; then the belayer would only need to see it, wrap it and then go fight off the bandits,
Then the climber can get to the top pull the sword out and become kind of Camelot!
I may have got my stories mixed up there...