Define dormant by behaviour rather than by feeling, and the definition depends on your business. For a service bought annually, six months of silence is normal. For a subscription, a month of no engagement is significant. The useful threshold is roughly twice your normal purchase or interaction interval, and applying a generic ninety day rule to a business with a long cycle produces campaigns to people who were never lapsed.
The message that works is a question rather than an offer. Asking whether their situation has changed, whether they still want to hear from you, or what they were hoping for when they first got in touch produces responses. An offer sent to somebody who has ignored you for eight months usually confirms that they are ignoring you, and it teaches you nothing about why.
Include an easy way to leave, prominently. This feels counterproductive and it is the most important part, because the alternative to somebody unsubscribing is somebody marking you as spam, and those two outcomes have very different consequences. Complaint rates are the fastest way to damage a sending domain, and dormant contacts are the group most likely to generate them.
Limit it to two or three messages and then act on the result. The purpose is to sort a list into people who are still interested and people who are not, and continuing to contact the second group indefinitely is what produces complaints. Somebody who does not respond to a re-engagement sequence has answered the question.
Then remove them, which is the step almost nobody takes. Carrying thousands of unengaged addresses depresses your deliverability for everybody else, costs money on platforms priced by list size, and makes your metrics unreadable. A smaller list of people who read what you send is worth considerably more than a large one that is mostly inert.
Segment by how they originally arrived before writing, because dormancy means different things depending on the source. Somebody who downloaded something and never engaged was probably never a prospect, while a past customer who has gone quiet is an entirely different conversation and deserves a different message. Sending both the same thing produces a message that fits neither.