If Eurostar is running late, they announce it on the train and train staff come through to sort people out.
SNCF are much better about this sort of thing than UK train operators. I've had the value of a non-changeable, non-transferable, don't-even-think-about-a-refund ticket credited to the cost of a replacement when I missed a TGV before, and missing it was entirely down to my own incompetence. I got lost in Nice and ended up in Monaco!!!