The css-break specification doesn't appear to define a lot of detail for the breaking of absolutely positioned elements. I would expect it to define a model that answers the following questions (and more) (all of which are written assuming writing-mode: horizontal-tb):

• does an absolutely positioned element (whose containing block is a fragmentainer or is inside a fragmentainer) fragment when it doesn't fit in a fragment of its container? (I assume it does.)
• are the top and bottom properties for absolute positioning relative to the entire sequence of fragments? Defined precisely how? If bottom is relative to the entire sequence, can parts of the element be in prior fragments to the one that contains the position of the bottom, and if so, how is bottom-relative fragmentation defined? (That is, what happens if there's no starting position that would produce the ending position exactly aligned with the bottom? And, for that matter, are implementations really expected to binary-search for such a starting position?)
• if an absolutely positioned element is in the last fragment and doesn't fit within that fragment, when does it overflow, and when does it create additional fragments, and when does it change the size of the fragmentainer? For example, does an absolutely positioned element with top: 500px; height: 200px inside of a container with column-count: 3; height: 200px; column-fill: auto cause the creation of a fourth (overflowing) column, or does it just overflow the third column? (For pages, I'd presume it's best to create a new page.)
• How do hypothetical boxes work, particularly if the hypothetical box is itself fragmented? (Is it interesting if the fragments of the hypothetical box have different widths?)