Quagmire, with a quick step-by-step from stable to less stable ones, made sure that if it ever collapsed, he would hold onto something hard and unmovable, which is typically rocks that are embedded into the ground. With each step taken, another look and glance from side to side, and each one is another thought and calculation into the mind itself. With precise thinking and calculation, he was able to make way further down, and eventually, given enough time, he was able to arrive at the bottom of the gigantic hole that sank earlier, due to the caves further in collapsing.
Upon arriving down the hole, almost immediately, he scanned the surroundings, all the while activating eagle's eye. This allowed him to scan and focus through the smallest opening and possible loophole that an enemy might use at a later date.