Subscriptions done through PayPal's Website Payments Standard are managed through PayPal. Subscriptions or recurring payments done through PayPal's Website Payments Pro are totally different. If the business you're dealing with uses PayPal's Website Payments Standard, then yes, they would have received an email notification of the cancellation and the same info would also be noted in their Account Transaction History. Note, also with Website Payments Standard, the subscription can be cancelled from within "your" PayPal Account.
If the business is using Website Payments Pro, then cancellation of the subscription via your PayPal Account would not be possible. You would need to contact the business and request them to ensure this is done.
Just some extra info that explains the differences between the products:
Website Payments Standard offers Recurring Payments or Subscriptions.
This service is managed/maintained by PayPal and "requires" the customer to have a PayPal Account. When the customer makes a Subscription purchase, he or she is redirected to PayPal. Once on the PayPal Screens the customer can either sign into their PayPal account, or they would pay with their credit card and during the process, create a PayPal account.
Recurring Payments is also a feature available through Website Payments Pro.
Recurring Payments is an automatic billing service you manage and maintain via your web site by using an application programming interface or API and requires a server-side programming using .NET, PHP, Java, etc. The Recurring Payments API is not the same as Subscriptions and Recurring Billing available for Website Payments Standard, or the Recurring Billing available for PayFlow Link or PayFlow Pro. When the customer makes a Recurring Payment purchase, he or she can pay with a credit card but, is not redirected to PayPal. The customer does not leave your web site where as you are passing the customer's credit card info to PayPal for authorization. Therefore you are controlling the customer experience. You can also offer the customer the option to pay with their PayPal Account if they so desire through the use of Express Checkout. Note, using Website Payments Pro, you will also be required to meet current Payment Card Industry or PCI compliance standards. Payment Card Industry Data Security Standards (PCI DSS) are network security and business practice guidelines adopted by Visa, MasterCard, American Express, Discover Card, and JCB to establish a "minimum security standard" to protect customer’s payment card information. This is a requirement for all merchants that store, transmit, or process payment card information. Pro is currently only available to US, UK and Canadian Accounts.
Regards,
skier
