In a past S&S group read, there's a post of JulieW in a thread discussing the possibility that Marianne sued Willoughby for a breach of promise. JulieW mentions that Lawrence Stone in his book The Road to Divorce concludes that there were three distinct types of plaintiffs in cases for breach of promise. One of those types I find that refers to what Lady R. could be fearing:

Second, there was the woman who exchanged promises of marriage in the future with a young man struggling to make his way in the world, and who remained chaste and faithful to him for several years, sometimes as many as six, and then learned that her lover had married someone else, sometimes by his own choice and sometimes under pressure from his parents and friends. The woman had rejected other suitors for many years and now found herself at a disadvantage on the marriage market at a fairly late age, a disadvantage for which she sought monetary compensation.

Suppose that Anne and Frederick got engaged, and they decided to wait until he earned his fortune. Then after several years, he found another woman and married her! (Of course we know that F. wouldn't do that, but Lady R. didn't know, and he could have been "under pressure from his family and friends". Remember "Lovers' vows"?). Or as LouiseH says, he could have died at sea.

Ironically, what Lady Russell feared that could happen to Anne if she got engaged, was really Anne's fate after she broke the engagement. Although, in this case, it was for lack of adequate suitors and not for being bounded by an engagement. Maybe if Charles Musgrove had been more intelligent, and were interested in other things apart from sports, like books, she could have accepted him.