I'm not sure how to phrase the question, but let's say you are running the Metropolis Algorithm and the distribution you are trying to produce is just a single distribution. Let's say the values of the distribution range between 0 and 100 and are discrete with step 1.
At each point, you have a 50% chance of making a decision of whether or not to move right or left. For example, if you are at 45, you have a 50% chance of making a decision on whether or not you want to go to point 46 and a 50% chance of making a decision on whether or not you want to go to point 44. The decision to actually go to an adjacent point is another probability decision but it's not important for this question.
My question is, what happens at point 0 or 100. At point 0, do you decide between point 100 and 1, or do you have a 100% chance of making a decision to go to point 1?
In other words, is the whole thing a circular loop?