The following pertains to Canadian passport renewal; YMMV for other passports:

The passport renewal form has a question that specifically asks if you want the expired/cancelled passport returned to you. I visited a local passport office last week to submit my application for a new passport, asking for my old passport to be returned to me. The clerk snipped the corner off the first couple of pages (the "important" ones), stamped cancelled on the "photo" page and then handed it back to me.

As far as Global Entry stickers are concerned, I have Global Entry (via my Nexus membership) and have never had a "sticker". My understanding is that these "stickers" are no longer required or even used anymore. Note that I have no idea how Global Entry works in the absence of Nexus membership, so it's possible that stickers may still be required in your passport in this case.

As noted above, once you receive your new passport you will have to update this information in GOES. You may also be required to present your passport at a local Nexus office (at least if you have Nexus membership) so that they can make a copy of it (there appears to be no clearly defined "rule" regarding this, hence the reason for saying "may be required"). Not sure how this works if you have Global Entry but not Nexus.