While that is the general perception, it is partly incorrect. Yes, mostly that is the way that people or companies get their ip address. However, private companies can (and do) own a block of ips. They are free to move them to a different isp. See:
That is the very nature of DHCP and has nothing to do with 'sticky'. With DHCP, the address is renewed once half of the lease has expired. This insures that as long as the address is not given up by the client, it will stay the same. Things that can trigger the lease being given up would be the lease expiring (client device turned off for term of lease), DHCP server being rebooted, or in some cases, the client being rebooted. I think sometimes these cable providers flush their DHCP servers and reboot end devices just to force the change and keep people from running home servers. My interpretation of sticky is that an address is married to a device or user independent of the DHCP parameters stated above. As I mentioned in a previous post, I do just that with a Windows VPN. The address is tied to a user, but they don't know the difference since they use DHCP. But, they will get the same address every time. I also have a Netscreen/Juniper VPN device which does the same thing.
Jim