How would someone secure an unconscious person with an injured leg to their horse? In my novel, a major character finds the MC on the side of the road, with a swollen/broken ankle, a few cuts and minor burns. He puts her on his horse and leads the horse home to fix her up. In another scene, she goes out looking for her daughter on her own when she is in need of rest etc. He is able to quickly track her down. They get into a bit of an argument that ends in "Well are you going to help or not?" Which they end up riding double. How would he secure her then if she isn't at full strength? Also, he or she would be holding crutches.
I'd guess they could ride double, with the injured person in front, so the other rider could hold on to her. Unconscious, you'd have to sling her over the saddle and, as you said, walk the horse to your destination.
Well.. for the first situation he could simply put her in front of him and securely hold her. If they both had belts he could tie them together. If he had rope he could tie her to himself. The crutches though... you'd have to have something to tie it down or just abandon them. You could try holding it like a lance, but there would be no real way to hold onto the injured person without some way to tie everything down. Without the proper materials on him... it'd be incredibly difficult.
Even riding double is uncomfortable pretty quickly, unless the saddle was too big for one rider to start with. Most double riding I've done has been bareback, and I wouldn't want to go far like that. You might need to look at size differentials - if this guy is super-big and the woman is super-small, it'd be easier for him to hold her on the horse. Slinging the woman over the saddle would be really uncomfortable (saddles are shaped to human butts, not human midriffs) and fairly dangerous unless the horse was very calm and the terrain was very flat and without obstacles. Horses shy to the sides fairly often, and they go through openings they know their bodies can fit, without too much concern for whether a human skull bulging out above their ribcage will be able to fit. Honestly, I think the most practical solution would be ditching the saddle and riding double both times, even when the woman's unconscious. Or better yet, making camp somewhere and nursing her until she's ready to sit upright. At which point the woman could ride and the man could lead the horse. If they're travelling any distance, the horse will be walking a lot of the time anyway, so having a human on foot wouldn't really slow them down much.
How long is she planning to be unconscious? Is it due to a head injury or blood loss? Long periods of unconsciousness sound kind of dangerous... I think I'd make her be able to stay awake. I've ridden a horse in a pretty bad shape. Once with a hugely swollen ankle. They probably just walk, so she could ride and he can walk the horse if she can't steer. Riding double with a saddle is tricky. Granted, I'm only familiar with English saddles. When we rode double, we did it without a saddle, but again, you need to have honed your balance enough to do it safely.. Securing someone on a horse sounds like a bad idea 'cause if the animal freaks out, rears, falls over etc. I wouldn't wanna be stuck on it, but then again, I'm paranoid. How weak is she anyway? If she can ride, she can sit in the saddle even if feeling a bit woozy. Better that than walking on her own feet.