If purusha never acts and is never changed by anything, the Samkhya account of bondage and liberation cannot be the ordinary story of a self trapped by matter and then freed from it, because nothing about purusha was ever actually altered in the first place. What the system describes instead is a case of mistaken identity. Purusha appears to suffer, to desire, to be born and to die only because it is mistaken for the intellect, the ego and the mind, the finest and most purusha-like layers of prakriti, which do think, desire and change. Bondage, on this account, is purusha failing to distinguish itself from those layers; liberation is purusha, through the discriminative insight the whole system exists to cultivate, recognising that it was never the one thinking or suffering at all.
This is why Samkhya's liberation, kaivalya, is described as isolation rather than union or extinction: purusha is not merged into anything greater, nor does it stop existing, it simply stands recognised as what it always was, uninvolved. The classical simile carries the point past the point of subtlety needed: a dancer who has been thoroughly seen has nothing left to perform, and withdraws; prakriti, once purusha's discrimination is complete, ceases to unfold for that purusha specifically, though it goes on producing appearances for every purusha that has not yet seen through it.
The system needs no god to accomplish this and states plainly that it has none, since the work is epistemic rather than devotional: getting a true description of what is which. That is also why Samkhya's vocabulary, purusha and prakriti above all, was borrowed wholesale by traditions that do posit a creator and had to refit the terms to a theology Ishvarakrishna's text never assumed.