I occasionally work with tables in Impress (and sometimes Draw).
When I select a table (e.g. selection rectangle around the table), and press the 'Delete' key - all the cells get cleared, but the table is not deleted. Pressing Delete again doesn't help.
This is already, I believe, a bug (and it is certainly inconsistent with the behavior of other objects on a slide).
If I select an additional object/element on the slide, however, and then press the Delete key - both elements get properly deleted. This is an additional inconsistency. It does not make sense that adding _more_ elements to a selection causes _less_ elements to remain from that selection after a keypress.
I don't think is very version-specific or platform-specific, but just in case:
I'm using LO 126.96.36.199 on Linux Mint 18.1, on an x86_64 machine.
*** This bug has been marked as a duplicate of bug 90518 ***
*** This bug has been marked as a duplicate of bug 78326 ***