[Voption]

I’m not the one to explain this, but briefly:
No, the count cannot fall below zero.
-sunspots have been tracked for a long time across history, and while the quality of our scientific-instruments has increased dramatically across time, by-convention they count the Sunspots using what has been a relatively stable methodology, procedure & agreement. (People have tried to manipulate the Data-set in the recent past.)

—see https://sohowww.nascom.nasa.gov/sunspots/
for information on the Solar & Heliospheric Observatory.
(and there are none visible right now)

[cyclotic]

Proud dad moment. My kid works on the SOHO satellite.