Unfortunately with Payments Standard, there are no features or options available for you to control the behaviour of the PayPal Shopping Cart "cookies". Although the data in the "cookies" does expire, the info can remain for up to 21 days. From your perspective, there's nothing you can do. It's up to the end user or customer to clear their browser's temp files, history and cookies.
If you want to control the customer's shopping experience, you may want to look into Payments Pro. With Pro, the customer remains on your web site or page. They are not redirected to the PayPal Checkout Screens. Payments Pro takes a bit of coding on your end and there is a monthly fee ($30.00) to use this product.
Some other options:
Payments Standard does have an inventory feature where as the system won't allow your customers to purchase more items than what's available. We use that feature all of time for our 1 of a kind items. Once an item is sold out, when the customer is on the Checkout Screen, they do get a notice that the item is unavailable and behind the scenes, the browser cookies are updated. Never had an problem with someone trying to order something that was not available. The drawback to this feature is that the customer is not aware of a sold out item until they proceed to the second page of the checkout process.
You may also want to look at a 3rd party shopping cart. Many carts have backend databases which manage the inventory and some even display the stock level on your web page or site. 3rd party carts can work with Payments Standard. They just do all the logic or management on your site or page and upload the end results to the PayPal Checkout Screens.
Basically Payments Standard is bare bones, has some good features and works quite well for many. However, if you have a need for more robust features, then either going with a 3rd party cart or switching to Payments Pro is your next level.
