Yes, the SEC can suspend a stock that no longer (or never) reports to the SEC as a shell stock, a.k.a. zombie ticker. The ticker would remain on the Grey Market until FINRA deletes the ticker as an inactive security.
Here is a linked post to one of the SEC's shell-expel sweeps. If you take a look at my replies to that post FINRA has deleted symbols 44 times from the SEC's suspensions on that date.
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