Google is feeling a bit philanthropic lately, but were not talking about extending life or anything crazy like that this time, rather were talking about replacing your broken phone for free no matter what happened to it. We're talking a refurbished device, not a brand spanking new one straight from the factory, but that hardly matters both considering refurbished phones are indistinguishable from new phones anyway, and it's way better than a cracked screen or water damaged phone anyway. Google now becomes part of an elite set of companies that offer free replacement of a device if something happens to it, which currently includes HTC and not a whole lot of others.
Google won't necessarily just give in and ship you a brand new phone though, there's a little bit of finagling that needs to be done after you call customer service. Once you give the customer service rep your IMEI number and tell them the problem, they'll likely tell you it's an out of warranty issue. Don't let that fool you though, as all you need to do is tell them that you've heard of people getting the phone exchanged with a replacement no matter what. After speaking with a supervisor you should be told that you're a valued customer and will receive a one time refurbished replacement. From there you'll have a hold placed on the credit or debit card you have on file with Google Play, and you'll have 21 days to ship the broken device back to Google after you've received the replacement device or else you'll get charged for another phone.
This is currently only for Nexus 5s that have been purchased through Google Play, so T-Mobile Nexus 5s and possibly Nexus 5s purchased used won't be eligible since you weren't the one who purchased it, but that's not a guaranteed barrier of entry. This comes as rumors of the Nexus X's launch in the coming month or so continue to swirl around and around, leaving us to wonder if Google is just trying to clear out stock of the Nexus 5 by giving them away to customers who need a new device.