Is there a system that can notify me once an abandoned gamer tag becomes available?

Just because the desired tag does not appear as in use in the Xbox system does not mean it is available for your use, as Gamertags are used by other Microsoft systems. If it is tied up, the only way a given account can become
available now is for the gamer who has that tag to change to something else.

Are you referring to a change in a particular gamer-tag name?

Every gamertag name is unique. Once it is taken it will not become available unless that person decides to change his/her nickname.

You can make your gamer tag similar to your desired nickname by adding additional characters or spaces

MS releases gamer tags in waves. There's no way to tell when the tag will become available. I can only advise to try everyday.

Hey there.

Not all consoles receive the update simultaneously. Once it becomes available for your console, it should notify you

It really is irrelevant if the system says the gamer tag is unavailable then you won't be able to use it until the system once again makes it available. You will need to keep checking or simply decide on a different tag. Good luck with choosing your new
tag.