Hi Katherine,
There are a few options:
1. Best option: have all departments ./ agencies working on the same parcel fabric. With this option everybody are always in vertical alignment, no setup is needed. Downside: requires everybody to be on the same network and/or host the geodatabase and clients on the cloud (which is basically a shared network)
2. If you are only interested in the vertical alignment and not so much on the data the other agency is creating, you can populate a global ID on all the points and then share the parcel fabric between the agencies. From now on the parcel points can be published as a feature service and consumed using in ArcMap. Use the Fabric Point Move To Feature
Add-in to move parcel points when they get updated between the parcel fabrics.
3. Geodatabase replication - this requires more effort to setup (network, permission, identical schemas) as well getting rid of relationship classes between parcel fabric classes. It also requires some one to physically sync and handle any conflicts. If both agencies are already on the same network they might as well use the first approach. With geodatabase versioning and appropriate QA processes in place the need for replication is questionable.