One item I've used more than once is a long, flat piece of lumber - I used to bring a couple of these to shooting locations, and I even added handles to the boards, for easy gripping and removal (after the fair damsel, I mean my models, were rescued). This type of device is one thing I wish I had with me when I was in the UK and Leila got stuck.
I found that a 6 inch wide, 3 foot long, 1 inch thick (roughly) piece of lumber would work fine. When the model got stuck, I (or an assistant) would go out to them, and place this behind them, providing leverage to pull oneself free.
I also brought poles, which could be inserted near the legs to help break up thick mud.
As Nessie already pointed out, keeping the person moving is key, otherwise the mud/quicksand can settle around the model, making extraction harder. So don't dally!!
Lastly, one must be aware of the thickness and not go too deep - avoidance of dangerous situations is the best preparation. That's why I liked working with experienced models - and, if working with a new model, I always paired her off with an experienced one. That is way many of my prior scenes did not have a submersion scene, or the model only sank to her chest and not up to her neck. We paused frequently during shooting of scenes to assess how the model was doing - if the mud/quicksand was too thick, we decided on no submersion or very deep sinking.
Many of you noted that my submersions were always short - no lingering blowing of bubbles, as in other producers videos. This was a safety feature - I wanted to make sure the model went under and came right back up, not getting stuck, and hence, not drowning. An interesting side story: Sarah Michelle and I shot last fall, after she had visited Dave, who has wonderful submersion scenes, but in the safety of his own- built sets. Well, Sarah did a submersion and did not rise right away - I nearly panicked and almost dove in after her. When she did pop up, she said she'd did long submersions for Dave, so why not for me!!! We quickly clarified the difference between real and simulated.
If you have specific questions for me, feel free to ask.
Mike