Tricky situation. Usually there is something you can eat, and I would try not to fret about some sugar, or chips for example, and semi primal things like rice or legumes or even homemade cake if it looked amazing.
But if they only have processed food I do think that's a little bizarre, I mean they haven't exactly gone to any trouble for you have they?
If you're sure it's going to happen again then I would eat at home first, just take the smallest helping of whatever and pick at it, push it round your plate and try not to let them notice you not actually eating it.
And it's not a bad idea to take something with you to "add" to the meal, it could end up being all you eat but at least you have shared it.