I believe the short answer is that it will then default to its normal flow in the document as though you hadn't applied any position, i.e. static positioning. So if the parent element happens to be 50px from the top and left of the document and position absolute or fixed, then the absolutely positioned child without positioning styling top/bottom/left/right would appear at 0, 0 relative to the parent, or 50px, 50px relative to the document. If you place the absolutely positioned element after a relatively positioned inline sibling, the element I believe should appear next to the inlined element, as though it has display: inline-block applied.
Best way to check is simply to try out some scenarios. Have a play around with various HTML layouts and CSS rules in Codepen or JSFiddle.