What happens to equity if a co-op evicts?

You have to look at the Proprietary Lease for the procedure in your particular Coop (and oddly the language on the back of the Stock Certificate).
That said, many Coops allow for a "Public or Private" sale and never underestimate how slimey a Coop's attorney will be to try and cheat a shareholder out of their equity.

Second 30 yrs response. Further- the co-op board and by extension their attorney- could be slimy.

What's the reason for eviction? Objectionable conduct? Failure to pay maintenance?

Leave it to Jared Kushner to explain it all (except the answer to OP's question): https://observer.com/2016/09/home-rule-getting-evicted-from-a-co-op-is-easier-than-you-realize/

Don't forget that the Coop needs no proof of any wrongdoing because under Pullman the court can't even question the facts.

CyJackX, do you need help?

I know of someone that was evicted from a coop, this person was AirBnBing their apartment, but claimed that a "roommate" was present so it was legal (of course this "legal" sublet was never approved by the coop). After several years of fighting and appealing eventually all appeals ran out and a sale was forced.

I don't really need any particular help, I was just curious! Whether a person gets whatever equity happens in a forced sale or if they got zilch!