Currently, if a recipient bounces they get hard blocked by Intercom. This means even if you send them an email via the Inbox, it won’t be sent to them and they won’t receive it. There is no obvious visual indication in Intercom that this has happened, so we’ve had examples where support reps have struggled to communicate with customers as their messages aren’t being received, with the customers sending messages annoyed about a lack of response.
After speaking with support, I’ve been advised to check the “Has hard bounced” user attribute in the sidebar. In reality, this is completely impractical to expect a support rep to check this field for every single chat they have, just in case the recipient has bounced.
Instead, it would be preferable if Intercom showed a prominent warning in the chat, advising the support rep that the person they are messaging is blocked, and advising them how to rectify this.