What happens when your Inactive National Guard annual status expires?

A couple of things you need to know about the ING, and should have been counseled on.
ING is intended for short term problems, like school, police academy, running up your own small business, extended medical care, etc. That's why it is intended for a year or less.
If you have no intention of returning to the unit, you need to transfer to a unit close to you, get a conditional release to contract to a Reserve unit near you, or request transfer to the IRR.
That said, ING doesn't run out by itself. Your unit is responsible for notifying you of a muster, relieving you from the ING, and having you report, either to return to duty or request a transfer to another unit or IRR, etc.
Continue to reach out to your unit, phone and email, and contact your BN S1, BDE S1, and if necessary, your state G1.
It is in your best interest to stay in front of this, because your unit AGRs are probably ignoring it because they don't understand the process, and they could get directed to schedule your muster on very short notice, maybe too short for you to get away from work, and that ends in an AWOL packet.
Either way, you need to ensure you are available for that muster, and read up on the way forward, which should be any one of the options listed above.

Meanwhile, if you weren't counseled going into ING, you need to read up on it now. The whole ING reg is only 36 pages, and can be found here:

https://www.ngbpmc.ng.mil/Portals/27/Publications/ngr/ngr%20614-1.pdf?ver=2018-09-07-082542-470

ING Soldiers are supposed to be contacted by their unit readiness no’s throughout their ING status. They also are required to send you a certified letter letting you know your time is about up. Now with that being said, you should have been counseled about your responsibilities to contact the unit monthly since full time manning changes frequently for various reasons and units are reorganized. If neither of these occurred that could be why you could have been forgotten until your name comes out on a report and the commander signs an arrest warrant. My guess is if you were concerned enough about returning you would have stayed in contact with the unit yourself.