In the Catholic Church, what are the options for a person whose spouse abandons them?

There's not a lot that can be done in this particular instance. One possibility is for Alice to argue that if Ben saw fit to leave, he didn't seem to be taking the marriage vows very seriously, and perhaps the marriage wasn't valid after all.

Catholicism regards marriage as including a permanent state of fidelity to one's spouse; Ben's leaving might be used to support an argument that at the time of the marriage, he didn't subscribe to this understanding of marriage. And canon law states that if one of the parties "marries" while intentionally meaning by marriage something different than the Church means, the relationship isn't a marriage:

If, however, either or both of the parties by a positive act of the will exclude marriage itself, some essential element of marriage, or some essential property of marriage, the party contracts invalidly.

(Canon 1102 sec. 2)

If Alice chooses to go this route and request a declaration of nullity in the marriage, the marriage tribunal is under the obligation to notify Ben and summon him to the ecclesiastical court within 20 days (canon 1507 sect. 2). If Alice has no idea of where Ben is—which may be the case; you don't specify—then it won't be possible to summon him. In this case it's possible for the judge to try and contact him, and, failing, issue a decree stating that all reasonable efforts to summon Ben have been made, and ordering the marriage tribunal to proceed.

If Ann does know where Ben lives (but simply can't communicate with him), a citation can be delivered to the address he's reasonably believed to live at. If Ben refuses to respond, but there is reasonable proof that the citation was delivered to him, the judge can declare Ben absent. This may allow the case to proceed without him. I don't know whether the law allows a declaration of nullity to be granted with Ben absent, much less whether it would be granted in the specific case. If it is, of course, Alice was never married and is free to if she desires.

If Alice chooses not to seek such a declaration, or if for whatever reason the declaration is not granted, then Alice is indeed married. She is unable to validly marry again, at least until Ben dies (canon 1085); nor can she enter a religious institute (canon 643, sec. 1, note 2).

However, she can request the local bishop to try to mediate in the affair:

Whenever there is hope of a favorable outcome, the judge is to use pastoral means to reconcile the spouses and persuade them to restore conjugal living.

(Canon 1695)

Indeed, this process should have started even before the annulment process:

Whenever the judge perceives some hope of a favorable outcome at the start of litigation or even at any other time, the judge is not to neglect to encourage and assist the parties to collaborate in seeking an equitable solution to the controversy and to indicate to them suitable means to this end, even by using reputable persons for mediation.

(Canon 1446 sec. 2, emphasis added)

If this is not successful, Alice can request an ecclesiastical decree of separation. There are a few situations in which the Church recognizes that abandonment of a spouse is the right of the other spouse: if the one spouse has committed adultery (canon 1152, sec. 1) or if "either of the spouses causes grave mental or physical danger to the other spouse or to the offspring or otherwise renders common life too difficult" (canon 1153 sec. 1). But if neither of these is the case (as appears in this instance), then Ben has wrongfully and maliciously abandoned Alice. If the bishop issues a decree of separation, it will account for the care of their children as well (canon 1154). It will require them to live out their lives in fidelity to the absent other, and to hope and pray for, and possibly try to work towards, reunification.