Hi Sebastian,
The choice is yours whether to close the position or not. If you remove an EA from your chart, the trade will stay open until SL or TP is hit. Once the EA is no longer on the chart, the strategy rules are no longer applied, but the SL / TP remains in place.
Personally, when I update my EAs on my live account, I close all positions, delete all EAs, load the new EAs into the platform, open new charts, and attach the new EAs to the charts.
Ilan