I used to keep an empty baby wipe container for that purpose. my kids aren't babies anymore so I don't have them handy. but yes, you're right. such a waste to have them dry out. I just add a little water to the pack.
When you say closed container do you mean the bag it came in or a separate container? I wouldn't take them out of the bag they came in because they came in that for a reason. The bags are specially made to hold a certain amount of moisture so that they don't dry out ( until they expire which is usually around over a year)
They do get dry but just the top ones but there's this little container for them to but them in and it keeps them wet or if they do try out just put a little water on them and it can still take off water proof mascara but I just recommend to buy the little container and u can use them at home or put in your purse and go!!