How could an estimator be biased but consistent according to mathematical definition?

Question

According to the definition, an estimator can be biased, if $E_{\theta}[\hat{\theta}]\ne\theta$, with $\theta$ as parameter for a distribution we want to get from samples. While the estimator can be consistent if $\hat{\theta}\overset{p}{\to}\theta$. How could an estimator be consistent but biased? In other words, how could it be, that $\hat{\theta}\overset{p}{\to}\theta$ may not lead to $E_{\theta}[\hat{\theta}]\ne\theta$?