They could keep a record and warn others, but likely won't bother.
The thing is, if a publisher renegws on a contract, it's a good thing for the author. A publishing contract includes an advance from the publisher in exchange for their sole right to publish your work (and spend money on doing so). This is calculated on the basis that it is the total of all royalties your work is expexted to earn. (And, realistically, most books don't even earn out their advances.)
If they choose not to publish a subsequent book they have contracted, it is because they have chosen not to spend the extra money on the publishing process. Were they forced to publish, they would put a minimum possible effort into promoting a book they didn't see as a good investment. If they are half-decent, you will get your advance without argument; at worst, a reminder or two of their obligations and the implicit threat of bad publicity will see you paid. And as they will have chosen not to publish,you get back the right to sell the manuscript to someone else for a second advance.
A good thing to get in your contract is thus a reversion clause on the first book(s) in the case where they choose to forego the subsequent book they have agreed to publish, especially if it's a series. That way, you can also resell the earlier books to someone else, boosting the compound value of the new book, as the right marketing could change the series' entire dynamic.