Assuming a collar strategy where I buy the underlying stock with a short call and long put option on it. Would the call be assigned away like a covered call, leaving the put option viable or would the put option disappear when the underlying is assigned away. (Put option's expiry date is further than the call option)
A long stock collar (aka collared stock) consists of long stock, a short OTM call and a long OTM put. Typically, both options are OTM though there's no rule that says that they must be. Conceptually, it consists of a covered call and a long protective put. If one of the options expires at a later date then the position would be considered a diagonalized long stock collar.
If the short call is assigned early, you are left with a long put. If you started with a diagonalized collar (your example) then regardless of when you are assigned on the covered call component (early or on the short call's expiration date), you are left with a long put with a later expiration.