Probably not. There are some rule-of-thumb guidelines about how many cases there should be, but either way 2 sounds like too little. You could try running it but there's a big chance that the standard errors, and thus the p-values, will be huge and uninterpretable.

Unfortunately, there is just not going to be enough variability in your dependent variable. It is hard to imagine a scenario in which it would be possible for you to enter any predictor in the model that will outperform the null model (which just predicts cases based on the modal category). 

It may be that you'll have to use an over-sampling strategy for the lower prevalence grouping/category to up the n, of course that is assuming it is even possible to do so. 

I agree with Matthew; and generally speaking, with a dataset like this, I don't think there's anything a regression coefficient could tell you that's any more informative than just saying "out of 82 patients, only 2 showed the outcome, and {they were both / one of them was and the other was / etc.}."

Hello Cinara.  In the terminology some authors use, you have 2 events (falls) and 80 non-events.  A general rule of thumb is that you should have 10-15 events per variable--or probably more accurately, per degree of freedom.  See Mike Babyak's nice article (link below) for more information.  HTH.

https://people.duke.edu/~mababyak/papers/babyakregression.pdf

Another way to think about it....

You can calculate the 95% confidence intervals of a binomial proportion.  In this case, the confidence intervals for 0/82, 1/82, and 2/82 all overlap quite a bit.  So there's really no statistical difference between those proportions.

You might be able to present the data this way if you have categories for your independent variable.  e.g. http://rcompanion.org/handbook/images/image093.png