Part of macOS
deletedStorage clean-up
○ Leave it
Frees space by removing caches macOS can rebuild.
What it is
When space runs low, it clears purgeable files such as old caches.
Why it might be busy
The disk is nearly full. Usually a few minutes.
If you stop it
macOS starts it again straight away. Leave it.
The verdict
○ Leave it. Part of macOS, or something that starts again by itself. You never need to close these.
In Activity Monitor
deleted
From Procession’s guide, in the words the app shows.