"You talk about what happens when catalogs go away. What happens to sales when a store goes away"?
When stores close, the dynamic between catalog and online sales isn't terribly exciting. Stores frequently operate in "isolation mode", meaning customers shop the store, but are unlikely to shop online, and very unlikely to shop in catalog.
When the store closes, maybe eighty percent of the store base simply won't shop online, or in catalogs, regardless of how powerful your brand is.
The other twenty percent seem to wait awhile, then slowly transition back to the online channel, or catalog channel (so long as the brand advertises to them via catalog).
The most interesting part of store closings happen in multi-store markets. In these instances, Multichannel Forensics provide a rich portrait of the interactions between customers and stores. If you close a store that is in "transfer mode", those customers will quickly shop another store, potentially boosting sales at the other store.
If you close a store that is in "isolation mode", well, then those sales are likely to be lost. That might be fine, especially if the store being closed is unprofitable.
So, when you're thinking of closing a store, take a look at what Multichannel Forensics tell you. Stores in "isolation mode" will result in lost sales when the store is closed. Stores in "equilibrium mode" will result in some sales being reallocated to other stores. Stores in "transfer mode" may send a large portion of their sales to another store. Don't expect magical things to happen online or in catalog when the store closes.