Doing some searching around, LME can go bad, but I don't know how much it would effect your beer if it's just a yeast starter. You apparently get what people have dubbed "Extract Twang" if the LME is shelved for too long, as well as the color of the extract darkens, but I'd imagine a yeast starter is insignificant enough in quantity that you probably don't have to worry much.
If I had to choose between the two, I'd say the canned is probably your best bet, as it sounds as though the plastic jar may be permeable to oxygen, therefor making it the least preserved over time between the two. I'd say use up the canned LME in your starters before using the plastic container, and if you don't notice any off smell/flavors with the canned starter/beer, you probably won't notice any issues with the plastic jar. That is of course, assuming the plastic jar isn't being re-opened and rotting from previous exposure to the elements.
Just bear in mind, I assume you won't use all of the extract in one starter, as soon as you open it, you're already at a disadvantage, so make sure the remaining extract is refrigerated, and used before very long after opening the old can/jar. While I'm guessing at this, I wouldn't hold onto it for more than 2 months after opening it, and even that seems to be a bit long.
Referencing:
Liquid malt extract storage
Can liquid malt extract go rancid