See description of an IMAP4 client side mail reader at Preferred IMAP settings
Client side caching of IMAP4 messages is a desirable feature for offline work e.g. travel disconnected from the server. Deletion operations can be invoked for the local copy or local/server. Mailbox synchronization on a subsequent connection will process server side deletes that are propagated back to the local cache
I use an Android phone with an IMAP4 client that behaves exactly this way. The same mailbox is accessible via webmail on my desktop browser. Propagation of server side deletes occurs exactly as described to the messages cached in my phone if deleted by the browser.
Assuming mailbox cleanliness was not a habit on the server side, the phone(s) that Huma and Hillary used to contact their IMAP4 server may very well have a huge local cache of messages for offline use. Backing the phone up to Weiner's laptop would capture a file of those messages that is no longer subject to remote management by a server side delete issued from the IMAP4 server.