A question about Irish Moss

If I were to cut out the dead stuff in the center of my Irish Moss clumps, would new green moss grow back in to fill the opening, or would I end up with a permanent hole in the center? Is it worth my effort to dig out the dead stuff from last year? I need a clear and accurate answer, please.

 

The common name "Irish Moss" is usually used for a seaweed, a marine algae. I'm assuming you are talking about a moss or other kind of terrestrial plant: Do you have the scientific name, or an alternative different common name for your plant? Thanks!
EDIT: I see a reference online to Sagina subulatata - is that it?

 

Yes. Sagina subulatata. It's used terrestrially as a ground cover between flagstones or steppingstones in garden footpaths. It produces very tiny white flowers in the Spring. It can develop dead patches in the center, especially after being buried under winter snow. I was wondering, if I cut out those dead patches, would the green stuff around them spread into the dug out areas and fill them in with new greenery? The peripheries have remained green, so the plants are still alive. This ground cover is good at spreading outward to some extent, so I would think it would also spread inward once the dead portions are removed. Can anyone say for certain this can happen?

My second question is, could those brown patches green up again on their own, if I leave them be? It might not be necessary to cut them out if they'll rejuvenate by themselves.

 

There shouldn't be any problem with it refilling the space, but you can accelerate the process by dividing the living parts and replanting in those areas (assuming that whatever caused the dead patch to happen won't re-occur, e.g., pet urine or heavily-compacted soil).