The PGP protocol is sometimes criticized because it lacks a feature called forward secrecy. Forward secrecy is intended to reduce or eliminate the effects of an attack that goes like this:
So starting out we are talking about a two phase attack that requires access to an end point and significant preplanning.
If we are talking about OpenPGP over email then creating an archive of your encrypted messages from monitoring the network is not really possible any more. Most email in transit is now separately encrypted on the network using TLS. The same situation exists for OpenPGP over XMPP.
So a practical attack would involve the compromise of not just your end point but your email server as well. The attacker would have to first compromise your email server, wait to build up an archive of your messages and then compromise your end device to get the secret key material to decrypt their archive. It would make more sense for an attacker to go for your end device in the first place and end up with the same material, sooner.
Email messages are normally kept indefinitely and that tends to be the default even on systems that provide forward secrecy. If the attacker gets your secret key material then they pretty much for sure are going to be able to get access to your archived messages at the same time. Very few people are willing to go without a message archive so forward secrecy is unlikely to help in most practical cases of messaging.
Reduced to the essence: forward secrecy is where you delete the encryption key protecting some encrypted data to prevent that key from falling into the possession of an attacker that already has that encrypted data. There is nothing preventing any system from doing that, even something based on the OpenPGP standard. For a practical demonstration see: A Demonstration of Message Burning Through Encryption using GnuPG.
Hardly anyone ever does forward secrecy with OpenPGP. Why not? It's easy to do in a technical sense and would not cause your correspondents to have to reverify your identity.
In 2020 a company called Cellebrite announced that they had a specific Signal Messenger data interpretation facility that would be useful in the event that their forensic box broke into the smartphone that Signal was running on1). This sort of attack could not reveal any messages archived off the network due to Signal's forward secrecy. Let's compare the end result to an encrypted email client running on the same phone using traditional passphrase protection:
|Archived Network Messages||Protected||Protected|
|Messages Saved on Phone||Revealed||Protected|
So the encrypted email actually ends up providing a better result for the user. That is because it is possible to lock up the encryption key more securely in practice with an offline medium than it is with an online, always available, medium like instant messaging. It seems possible that people don't bother with forward secrecy for encrypted email because they perceive it to be secure enough already. Forward secrecy might not be worth the extra effort for that particular medium.
In general the value of forward secrecy decreases as the protection of the secret key material increases. So it might be more important for situations like instant messaging where it is harder to protect the secret key material2). It might be very important for situations where the same secret key material is used by many users. For example it might be very worthwhile for an attacker to archive encrypted traffic from a messaging service used by millions of users protected by a single TLS private key if that service does not have forward secrecy.