That was from Nicotero or Kirkman IIRC on Talking Dead, about the zombies going into sort of hibernation and starving (but very, very slowly), but it's it's been shown in the show... The specific example pointed out as I recall it was the group in the diner, but every episode it's actually sort of shown... Zombies laying around, sleeping almost, then waking up when stirred. That's pretty common throughout the show. They're stirred up by anything from a mouse running by or a chopper flying overhead and they wake back up.
I seem to recall on a TD episode them also mentioning that the cold makes the zombies go a little more dormant, or slow down slightly, but they're still functional and with the right motivation are pretty much as deadly as usual.
Talking Dead serves a purpose with the right people on it...
I think the thought of them starving isn't really on the minds of the characters... So it's not a viable solution because it's never even considered really, but it's just mentioned because the question was asked whether they can starve... Ones locked up somewhere then probably could, eventually, but it could take eons, and they eat anything it seems so they seem to survive well and waiting them out till they exhausted everything alive on Earth that they eat isn't realistic anyway.
I was curious about this so I looked it up... Wikipedia sort of contradicts itself on them "sleeping". It says they're "playing dead" but that seems unlikely by the way the show implies them laying silent till something stimulates them and they wake up... They don't all wake up to attack. They simply wake up (as is evident at the diner place, and other settings).
Sometimes they wake up and strike immediately though, as with Herschel's leg... Sooooooooo, the wiki isn't reliable here I think.
They do mention they're starving though, even in the show, and it's likely that they'd waste away to nothing over time as the body basically devours itself if they go without food long enough in theory, or simply it rots away and eventually they re-die.
I think in the show it was Milton who mentions the starvation thing? I forget though. Him or Jenner.
I guess in the comics several times they come across zombies who've not eaten in a long time (including a child who starved to death himself, then came back and is now a starving zombie) who aren't even able to crawl and are barely "undead" at this point.
Zombies who don't eat seem to turn into "lurkers" though and go into that dormant state... Like the ones in the church which is still a scene I don't get... It looked like a wedding was taking place but everyone just sat down in a pew and died and was there that whole time.
Glen Mazarra said they don't starve, but eventually do rot away and die... sooooo, that's weird and kind of similar ultimately.