TapeAlert Code: 0x16, Type: Critical, Flag: EXPIRED CLEANING MEDIA,

The cleaning media can clean the drive 50 times. This is true for or all LTO drives except LTO1 (25 cleanings) . The tape has an NFC chip inside and this chip count the mounts of the tape.

So if a cleaning tape is mounted 50 times, it is expired and can not used again.

If a tape drive is in "cleaning required" state, then it will not work unless you mount to it a non expired cleaning media.

Unfortunately, you have to buy a new cleaning tape, if you want to use that tape.

A cleaning tape does not rewind like a data tape before it is ejected from the drive.

So, each time a cleaning tape is used, it will use a new piece on the tape. 
When the end of the tape is reached, the tape driver will report the messages that you have seen.

There is nothing you can do to use this tape.
Purchase new cleaning tape. And a spare.

*** EDIT ****

I have been corrected in a private discussion:

Rewind/no rewind of a cleaning tape depends on the drive type:

Eg. a 4mm/ DAT cleaning tape won't rewind - doesn't need to as the tape is completely encased in the cartridge with two reels.

An LTO will rewind as only one reel, otherwise it couldn't be ejected. However, I suspect (don't know for sure) that it 'forwards' to an 'unused' section of tape before it starts the cleaning cycle.