ṣ is optionally the substitute of the s of syand after the upasarga (Prepositions) anu , vi , pari , abhi and vi when the subject is not a living being.,
The root स्यन्दू प्रस्रवणे is anudatta. Thus अनुष्यन्दते । विष्यन्दते । परिष्यन्दते । अभिष्यन्दते तैलम् । निष्यन्दते । अनुस्यन्दते । विस्यन्दते । परिस्यन्दते ।
Why do we say 'when the subject is not a living being'? Observe अनुस्यन्दते मत्स्य उदके ॥ The option of this sutra will apply, when the subject is a compound of living and non-living beings. Thus अनुस्यन्देते or अनुष्यन्देते मत्स्योदके ॥ The subject here is a Dvandva compound, and it is not in the singular number because of 2.4.6. The word अप्राणिषु is a Paryudasa and not a Prasajya-pratishedha. If it be the latter sort of prohibition, then the force will be on the word living, and in a compound like मत्स्योदके, consisting of living and non-living beings, the prohibition will apply because it has a living being in it, and so there will be no षत्व ॥ In the other view, the force is on the word non-living, and because the compound contains a non-living being, therefore the option will be applied, and the presence of the living being along with it will be ignored.
The anuvritti of परि, नि and वि is understood here from 8.3.70. So these words could well have been omitted from the sutra, which might have then been अन्वभिभ्यांच स्यन्दतेरप्राणिषु, and by the force of च we would draw in the anuvritti of परि &c.,