You are worried about the fact that a candidate for a position with your firm has had many single year positions/jobs in theie past. How do I know you are worried? The fact that you are asking the question indicates that you are already uncomfortable with the candidate's history. That's a sign and if you have many qualified candidates without such a history, you might as well start with the people that don't make you nervous. But don't rule this person out completely, yet.
I will infer that either:
1) You would prefer that this candidate NOT join YOUR company for a single year, and then move to a new company.
2) You are not worried that the candidate would stay with your company for only one year. But you are worried that there are significant performance/competence problems with the candidate -- and that these short tenure positions reflect that kind of problem. This latter issue is a more serious concern, since -- even if you are okay with them working hard for a year, producing good results, and then moving on -- you don't know they wouldn't actually start to flounder after a few months, and then take the rest of the year to manage out of the company.
So, the simple answer to your question is "Yes, you should consider such a person, especially if a single year tenure would be useful to you. But you should not stop there. You need to dig deeper before you actually hire such a person."
After deciding that a year long tenure would be useful to you, there are a couple of key steps to take. If one year is not enough time, you should probably walk away from the candidate. However, to be thorough, you can proceed and perhaps be convinced that those tenures were an anomaly -- even though past performance is the best, if imperfect, predictor of future performance.
1) Talk with the candidate. Listen to their story of the manner in which they left each place. Dig. And Dig again. Ask hypotheticals: Would you have stayed "if...", etc. If you don't feel confident and cannot dig and hear enough details, and the kind of attitude that makes you feel confident in them is missing, walk away.
If you haven't walked away, yet, continue on:
2) Talk with references. Not just the official ones the candidate offers. But the unofficial ones. In this age of social media, you are unlikely to be more than 3 hops, and usually just two hops, separated from any candidate. Get "the skinny" that way. And if things don't match (in a positive sense) the good stuff have you learned so far -- and I know it's good stuff, otherwise you would have walked away and not gone to this step -- now is the time to walk away.
If, after all these steps -- you can accept a one year tenure, or you are convinced against odds that it won't be a one year tenure; you have confidence in the candidate's capabilities; you are okay with their story about the personal history which explains the past; and they "check out" via both formal and informal references -- you are still feeling like they are the right fit, you can be confident that you have don't everything possible to ensure she is a good candidate for your company.