Hi,
I apologise that you are facing an issue with InDesign.
I tried the issue you mentioned with the file that you had attached and was able to reproduce the problem. Also as mentioned by Uwe exporting the given document to IDML and then performing the same steps made the issue go away. I would recommend that you also give this a try and see if this solves your problem for now.
The last character is end of story character which is there in any text frame when you create it. The character in the document at the last is not part of the table but the story in which the table is inserted.
Also note that what you are trying (deleting the last character) deletes the table because there is no other character than the table in the last.
Regards
Javed