RC low pass filter difference with RC high pass filter
“Low pass” means below a certain frequency, the filter will not change the input to output transfer.   I guess you could say it “quits working” below a certain frequency, but I would not use this phrase.
“High pass” means below a certain frequency, it changes the input to output transfer ( making it smaller). So, I guess you could say, by definition, a high pass filter always “works”, ( that is, changes the transfer) at low frequencies.
So, if you use your definition of the word “works”, you are right!  Most people don’t think of it this way, though.