I recently stumbled across a quote of Fang-Hua Lin that I have trouble understanding [1, page 42].

It is a well-known fact that a weakly converging sequence of stationary integral currents may have a limit which is not a stationary current.

Question. How should I interpret this quote? What does Lin mean by a 'stationary current', and which sequence demonstrates this 'well-known fact'?

My initial guess would be that an integral current $T$ is 'stationary' if the varifold $\lvert T \rvert$ obtained by forgetting orientations is stationary. If I am not mistaken, this should mean that $\partial T = 0$? However my impression is that a flat limit $T$ would be 'stationary' in this sense of the word.

[1] F.-H. Lin. Mapping problems, fundamental groups and defect measures. Acta Math. Sin. 15 (1999), 25-52.