In such a case, Eurostar will have to rebook you on the next train with available seats. "Available” here is not subject to pass holder fare availability or even 2nd class availability (if your pass is 2nd class). Any empty seat will do. Without extra costs of course.
Also see EU Regulation 1371/2007, article 16.
Its likely via BRUssel-they are very well used to that there. And you´l not be the only 1 either. However-it may be a prob in the current hi-season with many trains fully booked-it may be that next connecting ICE is again also late and those seats then remain empty. At least talk to conductor so s/he can notify BRU about how many pax may be involved.
I know that with normal tickets they will book new tickets for you, due to the EU regulation and the Railteam agreement.
With Interrail I don’t know, but it should work the same. Eurostar staff is very friendly.