diff --git a/lisp/org-element.el b/lisp/org-element.el
index 29a90be41..e9f0b2c58 100644
--- a/lisp/org-element.el
+++ b/lisp/org-element.el
@@ -5745,8 +5745,11 @@ Providing it allows for quicker computation."
 			 (cbeg (org-element-property :contents-begin next))
 			 (cend (org-element-property :contents-end next)))
 		     (cond
-		      ;; Skip objects ending before or at POS.
-		      ((<= end pos)
+		      ;; Skip objects ending before point.  Also skip
+		      ;; objects ending at point unless it is also the
+		      ;; end of buffer, since we want to return the
+		      ;; innermost object.
+		      ((and (<= end pos) (/= (point-max) end))
 		       (goto-char end)
 		       ;; For convenience, when object ends at POS,
 		       ;; without any space, store it in LAST, as we
@@ -5764,7 +5767,9 @@ Providing it allows for quicker computation."
 				;; object, for consistency with
 				;; convenience feature above.
 				(and (= pos cend)
-				     (not (memq (char-before pos) '(?\s ?\t))))))
+				     (or (= (point-max) pos)
+					 (not (memq (char-before pos)
+						    '(?\s ?\t)))))))
 		       (goto-char cbeg)
 		       (narrow-to-region (point) cend)
 		       (setq parent next
diff --git a/testing/lisp/test-org-element.el b/testing/lisp/test-org-element.el
index 1bc2a5363..7b7eda3a6 100644
--- a/testing/lisp/test-org-element.el
+++ b/testing/lisp/test-org-element.el
@@ -3076,6 +3076,12 @@ Paragraph \\alpha."
    (eq 'bold
        (org-test-with-temp-text "* *bold*"
 	 (search-forward "bo")
+	 (org-element-type (org-element-context)))))
+  ;; Special case: incomplete cell at the end of a table row.
+  (should
+   (eq 'table-cell
+       (org-test-with-temp-text "|a|b|c"
+	 (goto-char (point-max))
 	 (org-element-type (org-element-context))))))