Part of this depends on what you mean by Spartan independence. That said, the short answer is that there wouldn’t have been many left in Sparta at that point. Epaminondas of Thebes invaded the Peloponnese in 370/69 BCE and as part of that expedition he freed the Messenian helots and helped them rebuild and fortify the ancient city of Messene to the west of Sparta. This was the home of the majority of the Spartan helot population and Sparta’s ability to be a society of more or less full time warriors was built on the back of the slave labor provided by the Messenian helots. While Sparta had very much fallen from the height of its power years before this, losing so many of their slaves in this way, arguably, took away any chance Sparta had of ever becoming a significant military power again. At this stage, I believe, the only helots remaining would have been in Laconia proper. These appear to have remained slaves, but I would imagine that with Spartan numbers significantly depleted by the war with Thebes and with the newly independent polis of Messene just down the road (so to speak), I think it likely that many of them took the first chance they could to leg it.

For more on this, I would direct you to Plutarch’s life of Pelopidas and Diodorus Siculus, Book 15.