It is not only forbidden to eat chameitz, there is also an obligation to get rid of all chameitz that is in one’s possession.
Biblically, one can relinquish ownership of chameitz that is in one’s possession and that would take care of the issue of owning chameitz. However, our sages were concerned that if one would have chameitz that is sitting around in one’s home they would inadvertently eat it. They therefore required one to remove all chameitz from one’s home. (We will discuss selling chameitz at a later time.)
It therefore follows that if one relinquishes ownership of the chameitz in their home they do not need to remove chameitz from locations that are very difficult to reach since there is no concern that one will inadvertently eat the chameitz there. Additionally, the rabbis concern was only about substantive food items, like a cookie. One need not worry about crumbs. For example, there is no obligation to move a fridge to remove chameitz from behind the fridge. (This is not the same as the prohibition against eating chameitz, which one would violate by even eating a crumb. For this reason, cleaning in the cooking/ dining area is different than cleaning anywhere else.)