Yes, it's possible you have none.

Some common types of soil bacteria can 'eat' it, and then 'poop' out either ammonia or nitrogen. I'm not sure how you're testing -- 'guess-strips' are never very accurate, and the stabilizer guess-strip test is the worst of them all.

An easy way to confirm no CYA is to
1. turn off your SWCG
2. add 5 ppm of chlorine via bleach (about 1.5 gallons of plain 6% household bleach) in the EVENING.
3. Test in the AM -- if chlorine is low, you have OTHER Problems.
4. Test that evening -- if it's a sunny or partly sunny day, and you have chlorine, you have stabilizer. If you have no stabilizer, you'll have no chlorine at the end of a sunny day.