You can keep anything that you did not order. I too am letting my subscriptions lapse -- one after 20+ years. This one company billed me for a new 5 year subscription -- and said it would automatically be renewed and I agreed to this by paying the current bill. I sent a letter that would blister your ears canceling that subscription.
A couple of other magazine companies have done something similar -- one continued the subscription for 6 months after it ended and then tried to collect. I pointed out that since I did not renew the subscription I was not responsible for anything they sent after the subscription was fulfilled. The only magazine I keep is National Geographic -- at least for now.
I guess they are hard up, but I want to be able to say yes or no to an extension of the subscription.