You can fight with your legs,with your shoulders, with your head, and with your mouth (assuming you can get close enough).
The caveat to this, of course, when it comes to the legs is being able to adjust your balance to fight with your hands bound. Martial combat utilizes the whole body for any technique, and the arms are an important part of balancing yourself when you’re on one leg. So, when your hands are tied behind your back, this disrupts their ability to balance themselves.
The other caveat to the legs is they are more difficult than the average hand to hand technique to master. They also don’t work as well in tight spaces unless you’re using a martial art designed for them such as Krav Maga, the martial art developed and used by the Israeli Defense Force.
It should be said, the first responsibility of a prisoner is to escape. If your character is in a position where they’re injured or trying to get away from their captors, they don’t have the time to be sitting around trying to take every opponent as they come nor should they want to. Unless they have some character flaw with a crazed need to prove themselves while fighting at an extreme disadvantage, their first priority is going to be getting away or getting their hands free so they can up their chances of survival.
This can ultimately be any kind of sequence you want, the old Jackie Chan and Jet Li movies often have fun over the top fight scenes where their trying to fend off multiple enemies while their hands are bound. It involves a lot of ducking, dodging, running, trying to free their hands, inevitably finding a way between using their opponent’s attacks (like with a sword) to cut their bindings, or something else before they can finally turn around and fight freely.
Usually, these sorts of scenes involve the character making use of their environment. (As all good fight scenes should.) Giving you a chance to show their cleverness and ability to innovate on the fly. An unarmed character with their hands bound isn’t going to have a lot of options against an enemy with a weapon, but they can utilize their environment do the fighting for them.
This can be simple stuff like using objects such as tables to separate them from their opponent, tricking their enemy into burying a sword in a chair instead of them, then kicking away the chair and disarming them, etc.
A more grounded sequence usually involves a bull rush breakout, stealth, playing dead, or sometimes just throwing yourself off a cliff.
The basic answer is: fight for flight. You don’t want to stick around while fighting at a disadvantage against people who have use of all their limbs, and probably weapons. Especially if it’s more than one person.
Don’t get caught up in the idea that skill is defined by winning, it isn’t. You can get about as far with social engineering as you can with violence. A character who is capable of risk assessment, and able to make choices based off their ability and environment is the way of showing a character knows what they’re doing. Sometimes, the choice really is escape so they can live to fight another day. When your character has a greater goal in mind, they really can’t afford to lose too much of their valuable time dispatching Mook Number 3. When your character is debating whether or not they’re going to fight, always ask: what do they get out of it versus the risks involved?
There’s a great episode in Justice League: Unlimited where Batman is caught by the Luthor’s evil league and he uses it as an opportunity to get intel and socially engineer the situation so they turn against each other.
There are lots of ways to take scenes like this which may not be immediately apparent, but are always opportunities to emphasize a character’s particular skill set.
Not everyone needs to be ripping out their captors’ jugulars with their teeth.
((I have bronchitis, so I apologize for everything being a little slow this week))