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It seems the show "Alcatraz" is destined for that long, inevitable walk to the execution chamber ... but one of the main stars tells TMZ ... the series is just too young to die!

Jonny Coyne -- the guy who plays Warden James on the show -- was grubbin' at the delicious Wood Ranch Grill in LA today -- when we informed him about the less-than-stellar ratings for last night's season finale.

Coyne tells us ... despite the numbers, the show is great ... and it would be "a shame" if it went to the chopping block ... especially because it allegedly does GREAT with people who own DVRs.