Falmer enslavement possible walkthrough:
So you've been enslaved by the falmer and you are now forced to do their biding. Big whoop. There are many ways you can escape your captors: you can run for it -- no one will stop you but that also means you leave your gear behind. You can incite other slaves to help you. They might provide a distraction or help you fight. You can misbehave so that your master will become wary of you: she's follow you everywhere because she does not trust you. You can use this opportunity to get the jump on her, recover the key to your restraint and to your belonging maybe. Or you can accept your life for a time and do as you are bid, there are 3 repeatable short slave quests to improve your master's disposition (which otherwise decrease steadily over time). If you decide to flee, you'll likely leave your gear behind. The falmers do not trade with the surface, so your gear will remain in the slave chest until you get it back. Will you find new weapons, armors and allies and mount an assault on Blackreach?

Vampire enslavement possible walkthrough:
You've been enslaved by vampire and transported into one of their main lair. Vampires are master illusionists and can put strong compulsion illusion spells on their captive. Indeed, you wake up with a geas on you which cause you to be dizzy and slowly lose consciousness the farther you are from your master. It also put a strong strain on your mental capabilities, reducing your magicka pool and regen. However, this geas has a weakness: to be able to maintain the spell continuously, the master has to bind it to a particular object (charm). If you get into possession of this charm, the geas is dispelled without anyone being the wiser. You now have options to escape.
Otherwise, one can always count on the Dawnguard to periodically raid vampire lairs across Skyrim. With a bit of luck, they can provide a distraction and with a lot of luck, even defeat your master and free you. Meanwhile, your master will partake to your sweet blood, with a risk of infection. Assuming you do get infected, you can let the disease progress until you turn, at which point you are welcomed amongst the rank of the undead and released to prey on mortals.

Soul trapped possible walkthrough:
This one is a bit simpler than the 2 previous scenarios. You've been soul trapped and you wake up inside a soul gem. However, unlike most mortal who suffer this fate, you do not fade away. You have two choices: Either bargain with the soulgem master at the center of the gem and solve his little riddle or wait for rescue (it shouldn't take more than a day of waiting). Once you get out, you'll realize that your soul has nonetheless been weakened by the experience and may need a few hours to recuperate.

Bandit ransom possible walkthrough:
You have been captured by bandit and their are holding you hostage for ransom. You can try to resist and unmake your restraints with the minigame. However, you may need to consider your surrounding first since it is not necessarily a good idea. The bandit will surely attack you on sight if you try to escape. On the other hand, if you have done some good deeds in this world, surely someone would gladly come to your aid and pay the ransom. If you haven't, then it is likely escape is your only option: Get ready for the best time to spring into action. There is a chance you'd be executed outside but bandits are clumsy, which might provide a good opportunity to escape since you'd then be under lighter guard.

Thalmor capture possible walkthrough:
Maybe you've been a long-time enemy of the Thalmor, or maybe you've just a knack for trouble. In any case, you've been transported to the main Thalmor prison in Skyrim: Northwatch Keep. You will be interrogated by a Thalmor inquisitor. Pay attention to what you say. Too much bravado may end up costing you your life. There are many topics of interrogation based on your progress in various questline. Assuming you are cooperative and not actively wanted, you should eventually be released to the custody of the Solitude jail system. You can then serve your remaining time. Otherwise, death by beheading is the usual punishment for high crimes against the Thalmor. You will need to make your escape before that, obviously.

NOTE: The most likely place the player will be defeated by thalmor is during the embassy quest. Therefore, I made sure that there is an alternative way to return to the embassy after the party scene is completed. You will receive a message via courier to inform you of the new route.

Tips regarding the minigame:
The minigame mechanics is used in a few escape. You need to rotate the ASDW keys clockwise (AWDS) or counterclockwise (ASDW) to wiggle free. However, there is a chance that the direction of rotation will change every few seconds and at every mistake. Also, wiggling consumes stamina and you’ll make mistakes at low stamina. Furthermore, the minigame, unlike the lockpicking minigame, takes place in real time so one has to be extra careful what is going on in the background or you might free yourself right when a guard is passing by -- that wouldn’t be good. Finally, the difficulty is related to your strength which is essentially your average weapon skill. Hence, mages will have a harder time and everyone will have a harder time at low level.

Miscellaneous:
-If you don’t know what is supposed to happen and nothing is happening, wait a few game hours. If nothing continue to happen, wait some more.