Depending on your state entering a property with a firearms prohibited sign is illegal.
Some states consider it trespassing.
You can also face jail time depending on the state.
Um, I'm pretty sure that unless they find out you are carrying (and when you're successfully carrying concealed, how would they know?), and then tell you to leave, you are not "trespassing" just because you're not in compliance with the rule they've enacted and perhaps posted.
And then, if they claim you are trespassing and you refuse to leave, a cop would have to witness you refusing to leave after being told to, in order to charge you with trespassing.
This would, you know, be about the only way that a person would be protected against a store manager calling the cops and announcing a trespasser, even though you were strolling through the store and no one had said a word to you. How would the cop know before he got there and saw the manager tell you to leave that the manager had already done so? If he truly hadn't, he could still lie to the cop and say he had. Would you like it if that were enough to get you arrested? A made-up story?
So far, I know that Texas has a very specific kind of sign that businesses must have in order to legally prohibit you from carrying inside. As I understand it, they are pretty rare, because companies don't want to piss off the large constituency that carries in Texas. (And that's a good thing.)