Interesting topic. My hunch is that most of the serious managers won't have players like this (maybe with the odd exception) since a player good enough to play in every regular season game is going to have some value left on the TL when they hit about 30 years old, and part of managing smartly is knowing when to sell a veteran before he loses are real value (and making sure he's replacement is already on board before you sell the old guy).
My team so far has had seven players with more than 300 games played for my team, and with the exception the active player still on my roster, I've sold them all off before they hit 32. My active player is about to turn 31, and you can sure that I'm already looking for his replacement since I have about one more season before the old guy's value drops under $400k.
Don't ask what sort of Chunks they are, you probably don't want to know. Blowing Chunks since Season 4!