Hi, you can model an entity that will be filled with the message "Claim Ownership" every time a new entry matches your condition. The check can be done with a job that scan the entity containing the entries and finds the name of the user in one of the attributes. You should add a column in that entity that stores whether the job has already processed a specific entry or not. Remember that the job is not directly connected to a user, so you must process every entry having "processed = 0" and match the name with a user and create the proper message.
Refer to this tutorial for learning how to model a job
https://my.webratio.com/learn/learningobject/scheduling-batch-operations-v-72
In the message board page then you model a list component with a relationship role condition stating that the message belongs to the logged in user.