Opened “please-take!” food items in a non-Jewish workplace

Question

Is it alright to consume unsupervised food items at work that are open and available to anyone, assuming the items were initially known to be Kosher¹ and there's no evidence of tampering?

Items that are commonly in this category might include:

• Sugar
• Coffee Creamer
• Ice
• Salad Dressing
• Sliced Raw Vegetables²

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^{1 Assuming it came sealed and marked Kosher, or someone reliable for Kashruth supervised or personally prepared the food}
_{2 Assuming the vegetables were known to have been cut with a Kosher/new knife on a Kosher/new cutting board and pose no other Kashruth problems (bugs, Tevel, etc.)}