Why would the IP be snatched? DHCP pools go from #0 to the end of the pool and -then- recycle. So if the pool is 256 IPs and you are customer number 76, you get (say) .77. As they add new customers, they grow up to 240. If somebody goes offline/online, they will request their existing IP to make the pool contiguous. If a -new- customer comes up and does not request a particular IP, they get the next available IP -- IP #241. So it goes until the pool is full. Once the pool has been allocated in its entirety, it will attempt to use not-currently-in-use IP addresses; this is oversubscription at the ISP level and is a really bad thing. Normally, they would expand the pool by a good 15-20% ... resulting in all of the existing customers getting the same IP over and over and over.
Generally, the only time that a device will get a different IP on an ethernet/dhcp network is if, for some reason, it loses track of what IP address it had the last time it was on. Then it will request the next available IP. Also, the ISP can force the DHCP server to not honor requests for particular IPs, which results in everybody getting new IPs the next time they reconnect. After the first connection, "dynamic" host control protocol usually isn't 🙂