A family of Microsoft relational database management systems designed for ease of use.
You can create code to do this. It's a great idea. One can never have too many backups. In fact, I rather think you should create incremental backups, not overwrite the previous backup. Why? If something goes wrong, there's a good chance the backup can also be corrupted. You want to be able to go back several generations, if needed.
You can use the Windows Task Scheduler to make backups of any files or folders, and that is a reasonable alternative as well.
Depending on how you are using Access, you may be able to handle the "backup on quit" task in a straightforward way. If you are talking about development sessions, it's a bit trickier than if you mean that you want users to be create backups when they quit.
Note that, in a properly designed Access database, the interface objects are split into a separate accdb from the tables containing data. Usually, in a working production situation, backing up the data is the higher priority. In development, it's probably a higher priority to keep a version history of your front end, interface, accdb.
I recommend a Version Control tool like https://github.com/joyfullservice for development. There are other options, including https://ivercy.com/
These tools allow you to keep track of your work in developing the database.
To get to a more specific consideration, it depends, in part, on whether you do mean development or production. In a production environment, where there can be multiple users making changes to the data in a shared back end, creating backups on close is not a good idea as it could lead to data loss if the back up interrupts another user's save of data.
And, unless you are simply referring to your own development, I think a disciplined use of a VCS is a better choice than simply doing a backup on close. That said, the way to do that could be to write a procedure to save the accdb as a copy and put that procedure in the close event of a hidden form. Open that form when the accdb starts and leave it hidden. When the accdb closes, it will close that form, triggering its backup code.
I guess we could discuss other aspects of the situation and focus on one more relevant tasks.