I have a repainting indicator but this is the way it works. Currently it leaves output arrows on the screen even when I set unstablePeriod to true and change previously drawn values in output array to NaN.

Is there any way around it?

what you mean by
The unstablePeriod mode is used for specific indicator, such as EMA, calculations.
Why do you think that previously calculated and drawn indicator values should change?

Well, I just need it for eyecandy. The signal been calculated and new data arrives and that very same signal moves to the new bar.

In metatrader there are a lot of repainting indicators like COG and others, so I wonder is it possible to do this in jforex with indicators engine. I am sure I can do it from within a strategy by adding and deleting objects, yet I wonder is it possible or will ever be possible from indicators.

The function setRecalculateAll will help you to do this.(https://www.dukascopy.com/swiss/docs/api/com/dukascopy/api/indicators/IndicatorInfo.html#setRecalculateAll(boolean))

indicatorInfo.setRecalculateAll(true);