There are a lot of different ways therapists and clients handle closure and transitions. There aren't many hard and fast rules about what should or can happen.
My own personal guideline (and that of many other clinicians) is this: what's in the best interest of the client.
Many decisions depend on the nature of the transition: how long the therapy was, why the therapy is ending/whose idea it was to end, what the quality of the therapeutic relationship is...
Sometimes people want to have the opportunity for some kind of ongoing contact- a way to check in periodically, for instance- and sometimes they don't have interest in that. Some therapists feels strongly that after a therapy ends there shouldn't be any contact; others feel in some cases it's a good idea.
Because there are a lot of variables involved, it's really important to thoroughly discuss transitions- any kind of transitions, not just ending therapy, but temporary breaks in therapy for maternity leave, weddings, illness, anything that necessitates a change in the status quo.
For temporary breaks it's a judgement call whether or not to see another clinician during the hiatus. Again, the issue is important to really talk about with your usual therapist. As SuperEgg points out, the support can be helpful while your therapist is away. And even though you won't have the same depth of relationship you do with your ongoing therapist, you still have the opportunity to continue your work. And finally, seeing someone else temporarily gives you a chance to talk about how the break is going for you.
As usual, the way to approach transitions is through our usual favorites: being scrupulously honest with ourselves, staying connected to ourselves and those we care about, and to ask for what we want and need.