This might depend on the issuer.

I don't have Chase experience, but I cancelled my Venture X at the very last minute (45 days after the annual fee was billed) in early April. Just for fun, I tried using that PP card over a month later in early May and I was let in without a second glance. The re-upped PP card showed (and still shows) a late March 2024 expiration date, and a late March 2023 issue date.

Speculating - it may be because I waited until after a new cardmember year was in effect (i.e. 30 days after annual fee billed) and Capital One just prepays for a year at a time.
I'm noticing my US Bank PPs whose cards I've cancelled less than a year ago but in 2022 also still show valid and a visit entitlement (like, 4 visits for Altitude Reserve). I'm gonna try these in the near future and see what happens.

I'm not very concerned about being billed because the accounts are very much closed. While there are PP terms about using PP cards after expiration, my PP cards are clearly not expired, so....