Do archived Web Billing subscription products keep renewing?

Hi all,

We changed the price of a Web Billing subscription product the way the docs suggest (we created new products and swapped them into our offering).

The old products are out of the offering, but they're still attached to our entitlement, because existing subscribers are on them.

We'd like to archive the old products to tidy up the catalog, but we couldn't find what that does to existing subscribers.

Questions:

1. If a product is archived, do its subscriptions keep renewing and keep their entitlement?
2. Does anything else change for those subscribers, like the customer portal or renewal emails?

Thanks!