I don't live in Germany, but I'm pretty sure they'll be another train available. Probably in about 30 minutes (or less if the train is so late that the next train has caught up with it). The inconvenience is having to get off of one train and onto another.
At least in the US, once a company has accepted you on your journey they have to eventually get you to your destination, or get you to agree to give up. One time the train even stopped and told people trying to make a connection to get out; they'd called taxis to meet the other train.