Side control on the bottom is a rough place to land. Defensive posture is crucial in order to survive, with most people opting for either double defensive frames, or an underhook with a frame under the chin. While most BJJ blue belts are well versed in traditional side control escapes (and, possibly, some guard maintenance), alternative defensive posture can sometimes be required in order to facilitate and escape (or just to survive!). What follows should be considered supplemental to a basic escape strategy (back to guard, hitting your knees), and in no way a replacement for the fundamentals. Having said that, sometimes you have to be extremely sneaky in order to get what you want in BJJ.
Here's one of my personal favorite defensive postures from side control. Conventional wisdom suggests that both defensive frames should be underneath, with one "frame" (elbow and forearm) across the waist, and the other underneath the chin. Unfortunately, your partner is likely to make this difficult to obtain, to say the least. In this particular situation, my right arm is in the right place, but my left arm is stuck on the outside (where my partner is likely to go for a spinning armlock or other high percentage submission). Right away, I'm looking to shoot my arm up and then latch on to my partner's far armpit. This will allow you to turn your partner's head away, making it extremely difficult to maintain good side control pressure, and opening up space for your inside knee to slide in. Once that inside knee is in, it's just a matter of inserting your butterfly hook on top. I'll frequently go right into a sweep from here (see How to Use Overhooks in Butterfly Guard for a reference on how to do this sweep), but you can just use the technique to escape from side control if you'd prefer.
In this next situation, instead of keeping still, your partner switches their hips to a modified kesa gatame position in response to your inside arm creeping in there to create space. This is a very common reaction (and a fantastic fundamental side control maintenance movement!), and one that you can reliably predict your opponent will go for. The trick to this technique is timing: as soon as your partner switches their hips, you need to grab the back of both of your knees. The easiest way to accomplish this is to rock your hips high into the air as you anticipate the hip switch. Once there, you can latch on to your knees and kick outward, propelling your body forward (and rocking your partner's body back). In a perfect world, you can end up on top in your own modified kesa gatame position, but even if your partner reacts back and you end up just creating some space, sometimes that's more than enough to initiate an escape from a tight side control. For other options from here, check out these Modified Kesa Gatame escapes.
Over the years, I've seen perhaps three dozen escapes from "100 Kilos" side control (when the person on top is blocking your hip and your head), and virtually all of them involve turning in to your partner and going for a tackle. This is, indeed, a classic and viable approach most of the time. However, when you're smaller than your opponent, or your opponent is fantastic at maintaining position, this approach can be virtually impossible. On the other hand, with proper frames, turning away can work out well for you.
This technique starts with building a frame underneath your opponent's near side shoulder, making sure that your right elbow (assuming your partner is on your right side) creeps underneath their armpit. Your left hand simply reinforces your right arm. You now have the ability to turn away from your partner, and indeed, many will simply go to their knees and then opt for an escape from turtle as an immediate follow up. However, if you're flexible, it is possible to build your base up onto your neck and shoulders as you're turning away, then swing your hips into your partner's direction, finally dropping your hips to the ground in between you and your partner. Note: you might have to go straight into a "double under" stack defense here, but you also might catch a triangle if your partner responds poorly.
This is a wildly unorthodox move that can actually catch people off guard, particularly if they've never seen it before. Here, you're going to start with a typical defensive frame across the hip on the near side, but your left arm is going to grab your partner's right wrist (once again, assuming they're on your right side here). While holding their wrist in place, you need to hip out and snake your left knee inside their elbow, creating a defensive frame that makes it difficult for them to put any weight on you. Your right foot can now sneak over the top, ultimately hooking underneath their wrist from above. Since your right foot has their wrist hooked, and tension is holding this system in place (from their shoulder ligaments, no doubt), you can easily hip out to the side by putting your right foot on the mat.
Here, Rudy (the black belt on the bottom) elects to add two elements in order to tighten the position up. First, once he has created the proper angle, he locks the arm in place by stepping back over with his right foot. This is particularly useful against a flexible, savvy opponent who will try to lift his or her arm up over your foot to escape. Second, he grabs the collar with his left hand, controlling the posture. In order to finish the submission, all that's left is to rotate the wrist up and back with your ankles. One quick second option on the finish: simply lift your hips straight up.
Remember: all of these escapes are predicated upon your partner understanding a couple of much more fundamental options: turning in toward them with defensive frames, or escaping to your knees (and, typically, going for a tackle). If your partner isn't aware of how those more basic options work, these alternative options can serve you well. Try them out over time, and, as always, please let me know how you enjoy these options, and whether they work for you!